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Professor Jose Felipe Voloch

Contact

Department: Mathematics and Statistics

Email: felipe.voloch@canterbury.ac.nz

Direct Dial: +64 3 3692427

Office: Jack Erskine 723

Languages: English, Portuguese

About
Research / Creative works
Networks

Fields of Research

  • Number Theory, Algebraic Geometry, applications to Coding Theory, Cryptography

Researcher Summary

My research is primarily in the area of Number Theory, which is the discipline that studies properties of the integers. In particular, I study Diophantine equations, which are polynomial equations in many variables whose solutions are sought among the integers. Algebraic Geometry is the area of Mathematics that studies the geometric objects defined by polynomial equations and they play a fundamental role in my research. A spinoff of this research consists of applications to Cryptography (the study of encryption, which protects information from malicious attacks) and Coding Theory (which is the study of methods for protecting telecommunication against random errors).

Subject Area: Disciplines

  • Mathematics: Pure Mathematics

Resources

  • Personal webpage

Research/Scholarly/Creative Works

Journal Articles
  • Creutz B. and Voloch JF. (2022) The Brauer-Manin obstruction for constant curves over global function fields. Annales de l'Institut Fourier 72(1): 43-58. http://dx.doi.org/10.5802/aif.3473.
  • Sheekey J., Van De Voorde G. and Voloch JF. (2022) ON THE PRODUCT OF ELEMENTS WITH PRESCRIBEDÂ TRACE. Journal of the Australian Mathematical Society 112(2): 264-288. http://dx.doi.org/10.1017/S1446788720000178.
  • Booher J. and Voloch JF. (2021) Recovering Affine Curves Over Finite Fields From L-Functions. Pacific Journal of Mathematics 314(1): 1-29. http://dx.doi.org/10.2140/pjm.2021.314.1.
  • Salgado C., Varilly-Alvarado A. and Voloch JF. (2021) Locally Recoverable Codes on Surfaces. IEEE Transactions on Information Theory 67(9): 5765-5777. http://dx.doi.org/10.1109/TIT.2021.3090939.
  • Shparlinski IE. and Voloch JF. (2021) Erratum: Value sets of sparse polynomials (Canadian Mathematical Bulletin (2020) 63 (187-196) DOI: 10.4153/xxxx). Canadian Mathematical Bulletin http://dx.doi.org/10.4153/S0008439521000928.
  • Voloch JF. (2021) Factoring polynomials over function fields. .
  • Barros R. and Voloch JF. (2020) Effect of variation in density on the stability of bilinear shear currents with a free surface. Physics of Fluids 32(2) http://dx.doi.org/10.1063/1.5133454.
  • Booher J. and Voloch JF. (2020) Recovering affine curves over finite fields from $L$-functions. Pacific J. Math. 314: 1-28.
  • Booher J. and Voloch JF. (2020) Recovering algebraic curves from L-functions of Hilbert class fields. Research in Number Theory 6(4) http://dx.doi.org/10.1007/s40993-020-00222-0.
  • Shparlinski IE. and Voloch JF. (2020) Value Sets of Sparse Polynomials. Canadian Mathematical Bulletin 63(1): 187-196. http://dx.doi.org/10.4153/S0008439519000316.
  • Voloch JF. (2020) Commitment Schemes and Diophantine Equations. .
  • Aubry Y., Herbaut F. and Voloch JF. (2019) Maximal differential uniformity polynomials. Acta Arithmetica 188(4): 345-366. http://dx.doi.org/10.4064/aa170806-11-7.
  • Creutz B. and Voloch JF. (2019) Tate-Shafarevich groups of constant elliptic curves and isogeny volcanos. arXiv.
  • Sutherland AV. and Voloch JF. (2019) Maps between curves and arithmetic obstructions. Contemporary Mathematics 722: 167-175. http://dx.doi.org/10.1090/conm/722/14532.
  • Bretèche RDL., Sha M., Shparlinski IE. and Voloch JF. (2018) The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves. Mathematische Zeitschrift 290(3-4): 831-855. http://dx.doi.org/10.1007/s00209-018-2042-0.
  • Creutz B., Viray B. and Voloch JF. (2018) The d-primary Brauer–Manin obstruction for curves. Research in Number Theory 4(2) http://dx.doi.org/10.1007/s40993-018-0120-3.
  • Shparlinski IE. and Voloch JF. (2018) Binomial exponential sums. arXiv.
  • Creutz BM. and Voloch JF. (2017) Local-global principles for Weil-Châtelet divisibility in positive characteristic. Mathematical Proceedings of the Cambridge Philosophical Society 163(2): 357-367. http://dx.doi.org/10.1017/S0305004117000032.
  • Ulmer D. and Voloch JF. (2017) On the number of rational points on special families of curves over function fields. New Zealand Journal of Mathematics 47: 1-7.
  • Amerik E., Kurlberg P., Nguyen KD., Towsley A., Viray B. and Voloch JF. (2016) Evidence for the dynamical Brauer-Manin criterion. Experimental Mathematics 25(1): 54-65. http://dx.doi.org/10.1080/10586458.2015.1056889.
  • Patrikis S., Voloch JF. and Zarhin YG. (2016) Anabelian geometry and descent obstructions on moduli spaces. Algebra and Number Theory 10(6): 1191-1219. http://dx.doi.org/10.2140/ant.2016.10.1191.
  • Voloch JF. (2016) Generators of finite fields with powers of trace zero and cyclotomic function fields. Portugaliae Mathematica 73(1): 65-70. http://dx.doi.org/10.4171/PM/1976.
  • Voloch JF. (2016) Planar surfaces in positive characteristic. São Paulo Journal of Mathematical Sciences 10(1): 1-8. http://dx.doi.org/10.1007/s40863-015-0011-7.
  • Shparlinski IE. and Voloch JF. (2014) Generators of Elliptic Curves over Finite Fields. Bulletin of the Institute of Mathematics Academia Sinica 9(4): 657-670.
  • Voloch JF. (2014) Differential descent obstructions over function fields. Proceedings of the American Mathematical Society 142: 3421-3424. http://dx.doi.org/10.1090/S0002-9939-2014-12189-7.
  • Voloch JF. and Zieve ME. (2014) Rational points on some Fermat curves and surfaces over finite fields. International Journal of Number Theory 10(2): 319-325. http://dx.doi.org/10.1142/S1793042113500954.
  • Farashahi RR., Fouque P-A., Shparlinski IE., Tibouchi M. and Voloch JF. (2013) INDIFFERENTIABLE DETERMINISTIC HASHING TO ELLIPTIC AND HYPERELLIPTIC CURVES. MATHEMATICS OF COMPUTATION 82(281) PII S0025-5718(2012)02606-8: 491-512.
  • Farashahi RR., Fouque PA., Shparlinski IE., Tibouchi M. and Voloch JF. (2013) Indifferentiable deterministic hashing to elliptic and hyperelliptic curves. Mathematics of Computation 82: 491-512. http://dx.doi.org/10.1090/S0025-5718-2012-02606-8.
  • Harari D. and Voloch JF. (2013) Descent obstructions and Brauer-Manin obstruction in positive characteristic. Journal of the Institute of Mathematics of Jussieu 12(3): 545-551. http://dx.doi.org/10.1017/S1474748012000758.
  • Shparlinski IE. and Voloch JF. (2013) Visible Points on Curves over Finite Fields. .
  • Conceição R., Ulmer D. and Voloch JF. (2012) Unboundedness of the number of rational points on curves over function fields. New York Journal of Mathematics 18: 291-293.
  • Voloch JF. (2012) Finite descent obstruction for curves over function fields. Bulletin of the Brazilian Mathematical Society, New Series 43(1): 1-6. http://dx.doi.org/10.1007/s00574-012-0001-7.
  • Faber X. and Voloch JF. (2011) On the number of places of convergence for newton's method over number fields. Journal de Theorie des Nombres de Bordeaux 23(2): 387-401. http://dx.doi.org/10.5802/jtnb.768.
  • Helm D. and Voloch JF. (2011) Finite descent obstruction on curves and modularity. Bulletin of the London Mathematical Society 43(4): 805-810. http://dx.doi.org/10.1112/blms/bdr015.
  • Voloch JF. (2011) Special divisors of large dimension on curves with many points over finite fields. Portugaliae Mathematica 68(1): 103-107. http://dx.doi.org/10.4171/PM/1882.
  • Ahmadi O., Shparlinski IE. and Voloch JF. (2010) Multiplicative order of gauss periods. International Journal of Number Theory 6(4): 877-882. http://dx.doi.org/10.1142/S1793042110003290.
  • Harari D. and Voloch JF. (2010) The Brauer-Manin obstruction for integral points on curves. Mathematical Proceedings of the Cambridge Philosophical Society 149(3): 413-421. http://dx.doi.org/10.1017/S0305004110000381.
  • Poonen B. and Voloch JF. (2010) The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Annals of Mathematics 171(1): 511-532. http://dx.doi.org/10.4007/annals.2010.171.511.
  • Voloch JF. (2010) Conics over function fields and the Artin-Tate conjecture. Houston Journal of Mathematics 36(3): 675-679.
  • Voloch JF. (2010) Elements of high order on finite fields from elliptic curves. Bulletin of the Australian Mathematical Society 81(3): 425-429. http://dx.doi.org/10.1017/S0004972709001075.
  • Farashahi RR., Shparlinski IE. and Voloch JF. (2009) On hashing into elliptic curves. Journal of Mathematical Cryptology 3(4): 353-360. http://dx.doi.org/10.1515/JMC.2009.022.
  • Silverman JH. and Voloch JF. (2009) A local-global criterion for dynamics on P1. Acta Arithmetica 137(3): 285-294. http://dx.doi.org/10.4064/aa137-3-8.
  • Ivanov P. and Voloch JF. (2008) Breaking the Akiyama-Goto cryptosystem.. IACR Cryptol. ePrint Arch. 2008: 284-284.
  • Shparlinski IE. and Voloch JF. (2008) Average distribution of prime ideals in families of number fields. Bulletin of the Brazilian Mathematical Society 39(3): 417-425. http://dx.doi.org/10.1007/s00574-008-0014-4.
  • Barreto PSLM. and Voloch JF. (2006) Efficient computation of roots in finite fields. Designs, Codes, and Cryptography 39(2): 275-280. http://dx.doi.org/10.1007/s10623-005-4017-5.
  • Hall C. and Voloch JF. (2006) Towards Lang-Trotter for elliptic curves over function fields. PURE AND APPLIED MATHEMATICS QUARTERLY 2(1): 163-178.
  • Mcguire G. and Voloch JF. (2005) Weights in codes and genus 2 curves. Proceedings of the American Mathematical Society 133(8): 2429-2437. http://dx.doi.org/10.1090/S0002-9939-05-08027-5.
  • Voloch JF. (2005) Computing the minimal distance of cyclic codes. Computational and Applied Mathematics 24(3): 393-398. http://dx.doi.org/10.1590/s1807-03022005000300004.
  • Voloch JF. (2005) On note on (k, n)-arcs. Discrete Mathematics 294(1-2): 223-224. http://dx.doi.org/10.1016/j.disc.2004.04.049.
  • Carlin ML. and Voloch J. (2004) Plane curves with many points over finite fields. Rocky Mountain Journal of Mathematics 34(4): 1255-1259. http://dx.doi.org/10.1216/rmjm/1181069798.
  • Helleseth T. and Voloch JF. (2004) Double circulant quadratic residue codes. IEEE Transactions on Information Theory 50(9): 2154-2155. http://dx.doi.org/10.1109/TIT.2004.833371.
  • Voloch JF. (2004) On some subgroups of the multiplicative group of finite rings. Journal de Theorie des Nombres de Bordeaux 16(1): 233-239. http://dx.doi.org/10.5802/jtnb.445.
  • Voloch JF. and Walker JL. (2003) Homogeneous weights and exponential sums. Finite Fields and their Applications 9(3): 310-321. http://dx.doi.org/10.1016/S1071-5797(03)00007-8.
  • Rodriguez Villegas F., Sadun L. and Voloch JF. (2002) Blet: A mathematical puzzle. American Mathematical Monthly 109(8): 729-740. http://dx.doi.org/10.2307/3072397.
  • Rodríguez Villegas F., Voloch JF. and Zagier D. (2001) Constructions of plane curves with many points. Acta Arithmetica 99(1): 85-96. http://dx.doi.org/10.4064/aa99-1-8.
  • Voloch JF. (2001) On the duals of binary BCH codes. IEEE Transactions on Information Theory 47(5): 2050-2051. http://dx.doi.org/10.1109/18.930939.
  • Kim M., Thakur DS. and Voloch JF. (2000) Diophantine approximation and deformation. Bulletin de la Societe Mathematique de France 128(4): 585-598. http://dx.doi.org/10.24033/bsmf.2383.
  • Vaaler JD. and Voloch JF. (2000) The least nonsplit prime in Galois extensions of ℚ. Journal of Number Theory 85(2): 320-335. http://dx.doi.org/10.1006/jnth.2000.2551.
  • Voloch JF. (2000) A note on the arithmetic of differential equations. Indagationes Mathematicae 11(4): 617-621. http://dx.doi.org/10.1016/S0019-3577(00)80030-0.
  • Voloch JF. (2000) Chebyshev’s method for number fields. Journal de Theorie des Nombres de Bordeaux 12(1): 81-85. http://dx.doi.org/10.5802/jtnb.266.
  • Voloch JF. (2000) Elliptic Wieferich primes. Journal of Number Theory 81(2): 205-209. http://dx.doi.org/10.1006/jnth.1999.2471.
  • Voloch JF. (2000) Jacobians of curves over finite fields. Rocky Mountain Journal of Mathematics 30(2): 755-759. http://dx.doi.org/10.1216/rmjm/1022009294.
  • Voloch JF. (2000) On a question of Buium. Canadian Mathematical Bulletin 43(2): 236-238. http://dx.doi.org/10.4153/CMB-2000-031-6.
  • Voloch JF. and Walker JL. (2000) Euclidean weights of codes from elliptic curves over rings. Transactions of the American Mathematical Society 352(11): 5063-5076. http://dx.doi.org/10.1090/s0002-9947-00-02637-4.
  • Scanlon T. and Voloch JF. (1999) Difference algebraic subgroups of commutative algebraic groups over finite fields. Manuscripta Mathematica 99(3): 329-339. http://dx.doi.org/10.1007/s002290050176.
  • Villegas FR. and Voloch JF. (1999) On certain plane curves with many integral points. Experimental Mathematics 8(1): 57-62. http://dx.doi.org/10.1080/10586458.1999.10504388.
  • Voloch JF. (1999) On the p-adic Waring's problem. Acta Arithmetica 90(1): 91-95. http://dx.doi.org/10.4064/aa-90-1-91-95.
  • Voloch JF. (1999) Plane curves and p-adic roots of unity. Bulletin of the Australian Mathematical Society 60(3): 479-482. http://dx.doi.org/10.1017/s0004972700036637.
  • Voloch JF. and Walker JL. (1999) Codes over rings from curves of higher genus. IEEE Transactions on Information Theory 45(6): 1768-1776. http://dx.doi.org/10.1109/18.782098.
  • Voloch JF. (1998) Differential Operators and Interpolation Series in Power Series Fields. Journal of Number Theory 71(1): 106-108. http://dx.doi.org/10.1006/jnth.1998.2241.
  • Voloch JF. (1998) Periods of ordinary abelian varieties in characteristic p. Bulletin of the Brazilian Mathematical Society 29(2): 295-300. http://dx.doi.org/10.1007/BF01237652.
  • Voloch JF. (1998) The Equation ax+by=1 in Characteristic p. Journal of Number Theory 73(2): 195-200. http://dx.doi.org/10.1006/jnth.1998.2295.
  • Felipe Voloch J. (1997) Distance functions on varieties over non-arciiimedian local fields. Rocky Mountain Journal of Mathematics 27(2): 635-641. http://dx.doi.org/10.1216/rmjm/1181071930.
  • Voloch JF. (1997) An analogue of the Weierstrass ζ-function in characteristic p. Acta Arithmetica 79(1): 1-6. http://dx.doi.org/10.4064/aa-79-1-1-6.
  • Voloch JF. (1997) Torsion points on y^2=x^6+1. .
  • Abramovich D. and Voloch JF. (1996) Lang's conjectures, fibered powers, and uniformity. New York Journal of Mathematics 2: 20-34.
  • Tate J. and Voloch JF. (1996) Linear Forms in p-adic Roots of Unity. International Mathematics Research Notices (12): 588-601.
  • Voloch JF. (1996) Integrality of torsion points on abelian varieties over p-adic fields. Mathematical Research Letters 3(6): 787-791. http://dx.doi.org/10.4310/MRL.1996.v3.n6.a7.
  • Voloch JF. (1996) Lang's conjecture in characteristic p: An explicit bound. Compositio Mathematica 103(1): 1-6.
  • Voloch JF. (1996) Transcendence of elliptic modular functions in characteristic p. Journal of Number Theory 58(1): 55-59. http://dx.doi.org/10.1006/jnth.1996.0060.
  • Buium A. and Voloch JF. (1995) Reduction of the Manin map modulo p. Journal fur die Reine und Angewandte Mathematik 1995(460): 117-126. http://dx.doi.org/10.1515/crll.1995.460.117.
  • Voloch JF. (1995) Curves that change genus can have arbitrarily many rational points. .
  • Voloch JF. (1995) Diophantine approximation in characteristie p. Monatshefte für Mathematik 119(4): 321-325. http://dx.doi.org/10.1007/BF01293591.
  • VOLOCH JF. (1995) DIOPHANTINE APPROXIMATION ON ABELIAN-VARIETIES IN CHARACTERISTIC-P. AMERICAN JOURNAL OF MATHEMATICS 117(4): 1089-1095. http://dx.doi.org/10.2307/2374961.
  • Voloch JF. (1994) RAMIFIED COVERS OF ABELIAN VARIETIES OVER FUNCTION FIELDS. MATHEMATICAL RESEARCH LETTERS 1(4): 465-467.
  • VOLOCH JF. (1994) SIEGEL THEOREM FOR COMPLEX FUNCTION-FIELDS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 121(4): 1307-1308. http://dx.doi.org/10.2307/2161247.
  • Voloch JF. (1994) Siegel's theorem for complex function fields. Proceedings of the American Mathematical Society 121(4): 1307-1308. http://dx.doi.org/10.1090/S0002-9939-1994-1209430-9.
  • Buium A. and Voloch JF. (1993) Integral points of abelian varieties over function fields of characteristic zero. Mathematische Annalen 297(1): 303-307. http://dx.doi.org/10.1007/BF01459503.
  • THAKUR DS. and VOLOCH JF. (1993) BEHAVIOR OF FUNCTION-FIELD GAUSS SUMS AT INFINITY. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 25: 417-426. http://dx.doi.org/10.1112/blms/25.5.417.
  • Voloch JF. (1993) Appendix to dinesh s. Thakur's â€behaviour of function field gauss sums at infinity’. Bulletin of the London Mathematical Society 25(5): 425-426. http://dx.doi.org/10.1112/blms/25.5.425.
  • Abramovich D. and Voloch JF. (1992) Toward a proof of the mordell-lang conjecture in characteristic p. International Mathematics Research Notices 1992(5): 103-115. http://dx.doi.org/10.1155/S1073792892000126.
  • ABRAMOVICH D. and VOLOCH JF. (1992) TOWARD A PROOF OF THE MORDELL-LANG CONJECTURE IN CHARACTERISTIC-P. DUKE MATHEMATICAL JOURNAL 66(2): 103-115.
  • Coleman RF. and Voloch JF. (1992) Companion forms and Kodaira-Spencer theory. Inventiones Mathematicae 110(1): 263-281. http://dx.doi.org/10.1007/BF01231333.
  • Garcia A. and Voloch JF. (1991) Duality for projective curves. Boletim da Sociedade Brasileira de Matemática 21(2): 159-175. http://dx.doi.org/10.1007/BF01237362.
  • Hefez A. and Voloch JF. (1991) Frobenius non-classical curves. Archiv der Mathematik 57(4): 416. http://dx.doi.org/10.1007/BF01198969.
  • Hirschfeld JWP., Storme L., Thas JA. and Voloch JF. (1991) A characterization of Hermitian curves. Journal of Geometry 41(1-2): 72-78. http://dx.doi.org/10.1007/BF01258509.
  • SILVERMAN JH. and VOLOCH JF. (1991) MULTIPLE WEIERSTRASS POINTS. COMPOSITIO MATHEMATICA 79(1): 123-134.
  • VOLOCH JF. (1991) A DIOPHANTINE PROBLEM ON ALGEBRAIC-CURVES OVER FUNCTION-FIELDS OF POSITIVE CHARACTERISTIC. BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE 119(1): 121-126. http://dx.doi.org/10.24033/bsmf.2160.
  • Voloch JF. (1991) On the conjectures of Mordell and Lang in positive characteristics. Inventiones Mathematicae 104(1): 643-646. http://dx.doi.org/10.1007/BF01245094.
  • Hefez A. and Voloch JF. (1990) Frobenius non classical curves. Archiv der Mathematik 54(3): 263-273. http://dx.doi.org/10.1007/BF01188523.
  • Voloch JF. (1990) Arcs in projective planes over prime fields. Journal of Geometry 38(1-2): 198-200. http://dx.doi.org/10.1007/BF01222904.
  • VOLOCH JF. (1990) EXPLICIT P-DESCENT FOR ELLIPTIC-CURVES IN CHARACTERISTIC P. COMPOSITIO MATHEMATICA 74(3): 247-258.
  • VOLOCH JF. (1990) MORDELL EQUATION IN CHARACTERISTIC 3. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 41(1): 149-150. http://dx.doi.org/10.1017/S0004972700017937.
  • Voloch JF. (1990) Mordell's equation in characteristic three. Bulletin of the Australian Mathematical Society 41(1): 149-150. http://dx.doi.org/10.1017/S0004972700017937.
  • Voloch JF. (1990) On the Completeness of Certain Plane Arcs-II. European Journal of Combinatorics 11(5): 491-496. http://dx.doi.org/10.1016/S0195-6698(13)80032-7.
  • Voloch JF. (1990) Primitive points on constant elliptic curves over function fields. Boletim da Sociedade Brasileira de Matemática 21(1): 91-94. http://dx.doi.org/10.1007/BF01236283.
  • VOLOCH JF. (1989) ON THE NUMBER OF VALUES TAKEN BY A POLYNOMIAL OVER A FINITE-FIELD. ACTA ARITHMETICA 52(2): 197-201. http://dx.doi.org/10.4064/aa-52-2-197-201.
  • Garcia A. and Voloch JF. (1988) Fermat curves over finite fields. Journal of Number Theory 30(3): 345-356. http://dx.doi.org/10.1016/0022-314X(88)90007-8.
  • Hirschfeld JWP. and Voloch JF. (1988) The characterization of elliptic curves over finite fields. Journal of the Australian Mathematical Society 45(2): 275-286. http://dx.doi.org/10.1017/S1446788700030172.
  • Vainsencher I. and Voloch JF. (1988) On the Castelnuovo-Severi inequality. Journal fur die Reine und Angewandte Mathematik 1988(390): 114-116. http://dx.doi.org/10.1515/crll.1988.390.114.
  • Voloch JF. (1988) A note on algebraic curves in characteristic 2. Communications in Algebra 16(4): 869-875. http://dx.doi.org/10.1080/00927878808823607.
  • VOLOCH JF. (1988) A NOTE ON ELLIPTIC-CURVES OVER FINITE-FIELDS. BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE 116(4): 455-458. http://dx.doi.org/10.24033/bsmf.2107.
  • Voloch JF. (1988) Diophantine approximation in positive characteristic. Periodica Mathematica Hungarica 19(3): 217-225. http://dx.doi.org/10.1007/BF01850290.
  • Garcia A. and Voloch JF. (1987) Wronskians and linear independence in fields of prime characteristic. Manuscripta Mathematica 59(4): 457-469. http://dx.doi.org/10.1007/BF01170848.
  • Stöhr KO. and Voloch JF. (1987) A formula for the Cartier operator on plane algebraic curves. Journal fur die Reine und Angewandte Mathematik 1987(377): 49-64. http://dx.doi.org/10.1515/crll.1987.377.49.
  • Voloch JF. (1987) On the Completeness of Certain Plane Arcs. European Journal of Combinatorics 8(4): 453-456. http://dx.doi.org/10.1016/S0195-6698(87)80052-5.
  • Stöhr KO. and Voloch JF. (1986) Weierstrass points and curves over finite fields. Proceedings of the London Mathematical Society s3-52(1): 1-19. http://dx.doi.org/10.1112/plms/s3-52.1.1.
  • Koutroufiotis D. and Voloch JF. (1985) Saddle surfaces admitting local support planes. Journal fur die Reine und Angewandte Mathematik 1985(358): 1-5. http://dx.doi.org/10.1515/crll.1985.358.1.
  • Voloch JF. (1985) Diagonal equations over function fields. Boletim da Sociedade Brasileira de Matemática 16(2): 29-39. http://dx.doi.org/10.1007/BF02584799.
  • GOMES JD. and VOLOCH JF. (1982) A GEOMETRIC INEQUALITY IN CRITICAL-POINT THEORY. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE 295(9): 535-537.
Chapters
  • Creutz B. and Voloch JF. (2021) Tate-Shafarevich groups of constant elliptic curves and isogeny volcanoes. In Shaska T; Moshe J (Ed.), Abelian varieties and number theory: 41-50.American Mathematical Society.
  • Voloch JF. (2013) Elements of high order. In Mullen G; Panario D (Ed.), Handbook of Finite Fields: 98-99. Boca Raton: CRC Press.
Conference Contributions - Published
  • Voloch JF. and Sutherland A. (2019) Maps between curves and arithmetic obstructions. In Aubry Y; Howe E; Ritzenthaler C (Eds). Contemporary Mathematics 722: 167-175. Providence, RI: American Mathematical Society. http://dx.doi.org/10.1090/conm/722.
  • Ivanov P. and Voloch JF. (2009) Breaking the Akiyama-Goto cryptosystem. In ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY 487: 113-118.
  • Voloch JF. (2004) Random diophantine equations. In.

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