Publications

V.Kumar Murty

By Subject :

Cryptography
  • Refinements of Miller's algorithm for computing the Weil/Tate pairing, (with I. Blake and G. Xu), J. Algorithms, to appear.
  • Non-linear secret sharing and prime numbers, to appear in: Discrete Mathematics and Applications, Proceedings of the 2004 Ettimadai conference, ed. M. Sethumadhavan.
  • Abelian varieties and Cryptography, in: INDOCRYPT 2005, pp. 1-15, ed. C. Veni Madhavan, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 2005.
  • Efficient algorithms for Koblitz curves over fields of characteristic three, (with I. Blake and G. Xu), J. Discrete Algorithms, 3 (2005), 113-124.
  • Counting points on an Abelian variety over a finite field, (with F. A. Izadi), in: INDOCRYPT 2003, pp. 323-333, eds. T. Johansson and S. Maitra, Lecture Notes in Computer Science 2904, Springer-Verlag, Berlin, 2003.
  • Abelian varieties - optimal cryptography for wireless communications ?, Wireless Security Perspectives, 2 (2000), 3-5.
Arithmetic of Abelian Varieties
  • Splitting of Abelian varieties: a new local-global problem, in: Algebra and Number Theory, pp. 258-268, ed. R. Tandon, Hindustan Book Agency, New Delhi, 2005.
  • The addition law on hyperelliptic Jacobians, in: Current Trends in Number Theory, eds. S. Adhikari, S. A. Katre and B. Ramakrishnan, pp. 101-110, Hindustan Book Agency, New Delhi, 2002.
  • Descending rational points on elliptic curves to smaller fields, (with A. Akbary), Canadian J. Math., 53 (2001), 449-469.
  • Base change and the Birch and Swinnerton-Dyer conjecture, (with M. Ram Murty) Papers in Honor of E. Grosswald, ed. M. Knopp, Contemporary Math., 143 (1993), 481-494.
  • The Albanese variety of a unitary Shimura variety (with D. Ramakrishnan), in: The Zeta Functions of Picard Modular Surfaces, (ed. R. Langlands, D. Ramakrishnan), CRM (1992), 445-464.
  • The Manin-Drinfeld theorem and Ramanujan sums, (with D. Ramakrishnan), Proc. Indian Acad. Sci., 97 (1988), 251-262.
Algebraic Cycles
  • Hodge and Weil classes on Abelian varieties, in: The Arithmetic and Geometry of Algebraic Cycles, pp. 83-115, eds. B. Gordon, J. Lewis and N. Yui, Kluwer Academic Publishers, Amsterdam, 2000.
  • Tate cycles on a product of two Hilbert modular surfaces, (with D. Prasad), J. Number Theory, 80 (2000), 25-43.
  • Computing the Hodge group of an abelian variety, in: Seminaire de theorie de Nombres Paris, (ed. C. Goldstein) Birkhauser-Verlag 1990, pp.141-158.
  • The Hodge group of an abelian variety, Proc. Amer. Math. Soc., 104 (1) (1988), 61-68.
  • Period relations and Tate's conjecture for Hilbert modular surfaces, (with D. Ramakrishnan), Inventiones Math., 89 (1987), 319-345.
  • Exceptional Hodge classes on certain abelian varieties, Math. Annalen, 268 (1984), 197-206.
  • Algebraic cycles on abelian varieties, Duke Math J., 50 (1983), 487-504.
Number Theory and Sieve Methods
  • Some results in number theory, II, in: Number Theory, eds. S. Adhikari, R. Balasubramanian and K. Srinivas, Ramanujan Math. Soc. Lecture Notes, 1 (2005), 51-55.
  • An application of sieve methods to elliptic curves, (with S. Ali Miri), in: INDOCRYPT 2001, pp. 91-98, eds. C. Pandu Rangan and C. Ding, Lecture Notes in Computer Science 2247, Springer Verlag, Berlin, 2001.
  • On the enumeration of finite groups, (with M. Ram Murty and P. Erdos). J. Number Theory, 25 (1987), 360-378.
  • On groups of squarefree order, (with M. Ram Murty), Math. Annalen, 267 (1984), 1090-1101.
  • The number of groups of a given order, (with M. Ram Murty), J. Number Theory, 18 (1984), 178-191.
  • On the density of various classes of groups, (with Ram Murty), J. Number Theory, 17 (1983), 29-36.
  • Some results in number theory I, (with Ram Murty) Acta Arith., 35 (1979), 367-371.
  • Irrational numbers arising from certain differential equations, (with M. Ram Murty), Canadian Math. Bull., 20 (1977), 117-120.
Analytic and Algebraic Number Theory
  • Estimates for sums of coefficients of Dirichlet series with functional equation, The Ramanujan Journal, 7 (2003), 225-235.
  • Splitting of primes in infinite extensions, in: Proceedings of the Millenial Conference on Number Theory, 2001, pp. 23-41, eds. A. Hildebrand, B. Berndt and N. Boston, A. K. Peters, Boston.
  • Class numbers of CM-fields with solvable normal closure, Compositio Math., 127 (2001), 273-287.
  • The least prime in a conjugacy class, Comptes Rendus Math. Rep. Acad. Sci. Canada, 22 (4) (2000), 129-146.
  • Average values of quadratic twists of modular L-functions, (with T. Stefanicki), Func. et. Approx., 28 (2000), 155-172.
  • A Tauberian estimate for sums of coefficients of Dirichlet series, Comptes Rendus Math. Rep. Acad. Sci. Canada, 21 (1999), 153-159.
  • Stark zeros in certain towers of fields, Math. Res. Letters, 6 (1999), 511-520.
  • Frobenius distributions and Galois representations, in: Automorphic Forms, Automorphic Representations and Arithmetic, ed. R. Doran, Z.-L. Dou and G. Gilbert, pp. 193-211, Proc. Symp. Pure Math., vol. 66, Part 1, Amer. Math. Soc., Providence, 1999.
  • Modular forms and the Chebotarev Density Theorem, II, in: Analytic Number Theory, pp. 287-308, ed. Y. Motohashi, London Math. Soc. Lecture Notes 247, Cambridge Univ. Press, 1997.
  • Bounded and finite generation of arithmetic groups, in: Number Theory, ed. K. Dilcher, pp. 249-261, CMS Conf. Proc., vol. 15, AMS, 1995.
  • The least prime which does not split completely, Forum Mathematicum, 6 (1994), 555-565.
  • Effective versions of the Chebotarev density theorem for function fields, (with J. Scherk), C. R. Acad. Sci. (Paris), 319 (1994), 523-528.
  • Strong multiplicity one for Selberg's Class, (with M. Ram Murty), C. R. Acad. Sci. (Paris), 319 (1994), 315-320.
  • Zeros of Dirichlet L-functions , (with R. Balasubramanian), Ann. Scient. Ecole Norm. Sup., 25 (1992), 567-615.
  • Mean values of derivatives of modular L-functions, (with M. Ram Murty) Annals of Math., 133 (1991), 447-475.
  • Non-vanishing of L-functions and their derivatives, Proc. Montreal Conf. on modular forms, (ed. R. Murty) Univ. of Montreal Press, 1990, pp. 89-113.
  • Holomorphy of Artin L-functions, in: Proc. Intl. Conf. on Ramanujan, Ramanujan Mathematical Society, 1989, pp. 11-24.
  • Zeros and poles of Artin L-functions, (with R. Foote), Math. Proc. Camb. Phil. Soc., 105 (1989), 5-11.
  • Lacunarity and modular forms, J. Indian Math. Soc., 57 (1988), 127-146.
  • Modular forms and the Chebotarev density theorem, (with M. Ram Murty and N. Saradha), Amer. Journal of Math., 110 (1988), 253-281.
  • The Euclidean algorithm for S-integers (with M. Ram Murty and Rajiv Gupta), CMS Conference Proceedings, 7 (1987), 189-201.
  • Odd values of the Ramanujan tau Function, (with M. Ram Murty and T.N. Shorey), Bulletin Math. Soc. France, 115 (1987), 391-395.
  • A variant of the Bombieri-Vinogradov theorem (with M. Ram Murty) CMS Conference proceedings, 7 (1987), 243-272.
  • Explicit formulae and the Lang-Trotter conjecture, Rocky Mountain J. Math., 15 (2) (1985), 535-551.
  • An analogue of the Erdos-Kac theorem for Fourier coefficients of modular forms, (with M. Ram Murty), Indian J. Pure and Appl. Math., 15 (10) (1984), 1090-1101.
  • Prime divisors of Fourier coefficients of modular forms, (with M. Ram Murty) Duke Math. J., 51 (1984), 57-77.
  • Fourier coefficients of modular forms, Proceedings of Matscience Number Theory conference, Lecture Notes in Mathematics, 1122, 163-172.
  • On the Sato Tate conjecture, Number Theory related to Fermat's last Theorem, ed. N. Koblitz, Birkhauser-Verlag, Boston, (1982), 195-205.
General and Expository
  • The work of Sarvadaman Chowla, (with M. Ram Murty and K. S. Williams), pp. 7-25, in: The Collected Works of S. Chowla, eds. J. Huard and K. Williams, CRM, Montreal, 2000.
  • Fermat's Last Theorem, in: Analysis, Geometry and Probability, pp. 125-139, ed. R. Bhatia, Hindustan Book Agency, New Delhi, 1996.
  • Modular elliptic curves, in: Seminar on Fermat's Last Theorem, ed. K. Murty, pp. 1-38, CMS Conf. Proc., vol. 17, AMS, 1995.
  • Report on Fermat's Last Theorem, Current Science, 67 (2) (1994), 82-88.
  • Ramanujan and Harish-Chandra, Math. Intelligencer, 15 (1993), 33-39.
  • The notion of a Shimura variety, in: Advances in Number Theory, ed. F. Gouvea and N. Yui, Oxford University Press, 1993, 195-212.
By Year :

1977
  • Irrational numbers arising from certain differential equations, (with M. Ram Murty), Canadian Math. Bull. 20 (1977), 117-120.
1979
  • Some results in number theory I, (with Ram Murty) Acta Arith., 35 (1979), 367-371.
1982
  • On the Sato Tate conjecture, Number Theory related to Fermat's last Theorem, ed. N. Koblitz, Birkhauser-Verlag, Boston, (1982), 195-205.
1983
  • On the density of various classes of groups, (with Ram Murty), J. Number Theory, 17 (1983), 29-36.
  • Algebraic cycles on abelian varieties, Duke Math J., 50 (1983), 487-504.
1984
  • An analogue of the Erdos-Kac theorem for Fourier coefficients of modular forms, (with M. Ram Murty), Indian J. Pure and Appl. Math., 15 (10) (1984), 1090-1101.
  • On groups of squarefree order, (with M. Ram Murty), Math. Annalen, 267 (1984), 1090-1101.
  • The number of groups of a given order, (with M. Ram Murty), J. Number Theory, 18 (1984), 178-191.
  • Prime divisors of Fourier coefficients of modular forms, (with M. Ram Murty) Duke Math. J., 51 (1984), 57-77.
  • Fourier coefficients of modular forms, Proceedings of Matscience Number Theory conference, Lecture Notes in Mathematics 1122, 163-172.
  • Exceptional Hodge classes on certain abelian varieties, Math. Annalen, 268 (1984), 197-206.
1985
  • Explicit formulae and the Lang-Trotter conjecture, Rocky Mountain J. Math., 15 (2) (1985), 535-551.
1987
  • The Euclidean algorithm for S-integers (with M. Ram Murty and Rajiv Gupta), CMS Conference Proceedings, 7 (1987), 189-201.
  • Odd values of the Ramanujan tau Function, (with M. Ram Murty and T.N. Shorey), Bulletin Math. Soc. France, 115 (1987), 391-395.
  • On the enumeration of finite groups, (with M. Ram Murty and P. Erdos). J. Number Theory, 25 (1987), 360-378.
  • Period relations and Tate's conjecture for Hilbert modular surfaces, (with D. Ramakrishnan), Inventiones Math., 89 (1987), 319-345.
  • A variant of the Bombieri-Vinogradov theorem (with M. Ram Murty) CMS Conference proceedings, 7 (1987), 243-272.
1988
  • The Manin-Drinfeld theorem and Ramanujan sums, (with D. Ramakrishnan), Proc. Indian Acad. Sci., 97 (1988), 251-262.
  • Lacunarity and modular forms, J. Indian Math. Soc., 57 (1988), 127-146.
  • Modular forms and the Chebotarev density theorem, (with M. Ram Murty and N. Saradha), Amer. Journal of Math., 110 (1988), 253-281.
  • The Hodge group of an abelian variety, Proc. Amer. Math. Soc., 104 (1) (1988), 61-68.
1989
  • Holomorphy of Artin L-functions, in: Proc. Intl. Conf. on Ramanujan, Ramanujan Mathematical Society, 1989, pp. 11-24.
  • Zeros and poles of Artin L-functions, (with R. Foote), Math. Proc. Camb. Phil. Soc., 105 (1989), 5-11.
1990
  • Computing the Hodge group of an abelian variety, in: Seminaire de theorie de Nombres Paris, (ed. C. Goldstein) Birkhauser-Verlag 1990, pp.141-158.
  • Non-vanishing of L-functions and their derivatives, Proc. Montreal Conf. on modular forms, (ed. R. Murty) Univ. of Montreal Press, 1990, pp. 89-113.
1991
  • Mean values of derivatives of modular L-functions, (with M. Ram Murty) Annals of Math., 133 (1991), 447-475.
1992
  • The Albanese variety of a unitary Shimura variety (with D. Ramakrishnan), in: The Zeta Functions of Picard Modular Surfaces, (ed. R. Langlands, D. Ramakrishnan), CRM (1992), 445-464.
  • Zeros of Dirichlet L-functions , (with R. Balasubramanian), Ann. Scient. Ecole Norm. Sup., 25 (1992), 567-615.
1993
  • Ramanujan and Harish-Chandra, Math. Intelligencer, 15 (1993), 33-39.
  • The notion of a Shimura variety, in: Advances in Number Theory, ed. F. Gouvea and N. Yui, Oxford University Press, 1993, 195-212.
  • Base change and the Birch and Swinnerton-Dyer conjecture, (with M. Ram Murty) Papers in Honor of E. Grosswald, ed. M. Knopp, Contemporary Math., 143 (1993), 481-494.
1994
  • The least prime which does not split completely, Forum Mathematicum, 6 (1994), 555-565.
  • Report on Fermat's Last Theorem, Current Science, 67 (2) (1994), 82-88.
  • Effective versions of the Chebotarev density theorem for function fields, (with J. Scherk), C. R. Acad. Sci. (Paris), 319 (1994), 523-528.
  • Strong multiplicity one for Selberg's Class, (with M. Ram Murty), C. R. Acad. Sci. (Paris), 319 (1994), 315-320.
1995
  • Bounded and finite generation of arithmetic groups, in: Number Theory, ed. K. Dilcher, pp. 249-261, CMS Conf. Proc., vol. 15, AMS, 1995.
  • Modular elliptic curves, in: Seminar on Fermat's Last Theorem, ed. K. Murty, pp. 1-38, CMS Conf. Proc., vol. 17, AMS, 1995.
1996
  • Fermat's Last Theorem, in: Analysis, Geometry and Probability, pp. 125-139, ed. R. Bhatia, Hindustan Book Agency, New Delhi, 1996.
1997
  • Modular forms and the Chebotarev Density Theorem, II, in: Analytic Number Theory, pp. 287-308, ed. Y. Motohashi, London Math. Soc. Lecture Notes 247, Cambridge Univ. Press, 1997.
1999
  • A Tauberian estimate for sums of coefficients of Dirichlet series, Comptes Rendus Math. Rep. Acad. Sci. Canada, 21 (1999), 153-159.
  • Stark zeros in certain towers of fields, Math. Res. Letters, 6 (1999), 511-520.
  • Frobenius distributions and Galois representations, in: Automorphic Forms, Automorphic Representations and Arithmetic, ed. R. Doran, Z.-L. Dou and G. Gilbert, pp. 193-211, Proc. Symp. Pure Math., vol. 66, Part 1, Amer. Math. Soc., Providence, 1999.
2000
  • Abelian varieties - optimal cryptography for wireless communications ?, Wireless Security Perspectives, 2 (2000), 3-5.
  • The least prime in a conjugacy class, Comptes Rendus Math. Rep. Acad. Sci. Canada, 22 (4) (2000), 129-146.
  • The work of Sarvadaman Chowla, (with M. Ram Murty and K. S. Williams), pp. 7-25, in: The Collected Works of S. Chowla, eds. J. Huard and K. Williams, CRM, Montreal, 2000.
  • Average values of quadratic twists of modular L-functions, (with T. Stefanicki), Func. et. Approx., 28 (2000), 155-172.
  • Hodge and Weil classes on Abelian varieties, in: The Arithmetic and Geometry of Algebraic Cycles, pp. 83-115, eds. B. Gordon, J. Lewis and N. Yui, Kluwer Academic Publishers, Amsterdam, 2000.
  • Tate cycles on a product of two Hilbert modular surfaces, (with D. Prasad), J. Number Theory, 80 (2000), 25-43.
2001
  • An application of sieve methods to elliptic curves,(with S. Ali Miri), in: INDOCRYPT 2001, pp. 91-98, eds. C. Pandu Rangan and C. Ding, Lecture Notes in Computer Science 2247, Springer Verlag, Berlin, 2001.
  • Splitting of primes in infinite extensions, in: Proceedings of the Millenial Conference on Number Theory, 2001, pp. 23-41, eds. A. Hildebrand, B. Berndt and N. Boston, A. K. Peters, Boston.
  • Class numbers of CM-fields with solvable normal closure, Compositio Math., 127 (2001), 273-287.
  • Descending rational points on elliptic curves to smaller fields, (with A. Akbary), Canadian J. Math., 53 (2001), 449-469.
2002
  • The addition law on hyperelliptic Jacobians, in: Current Trends in Number Theory, eds. S. Adhikari, S. A. Katre and B. Ramakrishnan, pp. 101-110, Hindustan Book Agency, New Delhi, 2002.
2003
  • Counting points on an Abelian variety over a finite field, (with F. A. Izadi), in: INDOCRYPT 2003, pp. 323-333, eds. T. Johansson and S. Maitra, Lecture Notes in Computer Science 2904, Springer-Verlag, Berlin, 2003.
  • Estimates for sums of coefficients of Dirichlet series with functional equation, The Ramanujan Journal, 7 (2003), 225-235.
2005
  • Refinements of Miller's algorithm for computing the Weil/Tate pairing, (with I. Blake and G. Xu), J. Algorithms, to appear.
  • Non-linear secret sharing and prime numbers, to appear in: Discrete Mathematics and Applications, Proceedings of the 2004 Ettimadai conference, ed. M. Sethumadhavan.
  • Abelian varieties and Cryptography, in: INDOCRYPT 2005, pp. 1-15, ed. C. Veni Madhavan, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 2005.
  • Splitting of Abelian varieties: a new local-global problem, in: Algebra and Number Theory, pp. 258-268, ed. R. Tandon, Hindustan Book Agency, New Delhi, 2005.
  • Efficient algorithms for Koblitz curves over fields of characteristic three, (with I. Blake and G. Xu), J. Discrete Algorithms, 3 (2005), 113-124.
  • Some results in number theory, II, in: Number Theory, eds. S. Adhikari, R. Balasubramanian and K. Srinivas, Ramanujan Math. Soc. Lecture Notes, 1 (2005), 51-55.
Submitted
  • A note on the Window tau-NAF algorithm, (with I. Blake and G. Xu), submitted, 2004.
  • A variant of Lehmer's conjecture, submitted 2004.
  • Nonadjacent radix-tau expansions of integers in Euclidean imaginary quadratic number fields, (with I. Blake and G. Xu), submitted 2005.
In Preparation
  • Encryption of stored data in networks: Analysis of a tweaked block cipher (with I. Blake, C. Guyot and C. Kent), to be submitted.
  • Bounded generation for SLn(n ≥ 2) and Sp2n(n≥ 1), (with D. Loukanidis), to be submitted.
  • On the Sato-Tate conjecture II, in preparation.
  • Splitting of Abelian varieties, (with V. Patankar), in preparation.
  • Pair correlation and the Chebotarev density theorem, (with M. Ram Murty), in preparation.
  • On the order of vanishing of L-functions at the central critical point, (with M. Ram Murty), in preparation.
  • Satake compactifications and the congruence subgroup problem, (with J. Scherk), in preparation.
  • Semiregular cycles on Abelian varieties, in preparation.
  • Frobenius distributions and Galois representations: Numerical evidence, (with K. James and C. Mehta), in preparation.
  • Elliptic curve discrete logarithm problem and the lifting problem, (with S.Ali Miri),in preparation.
  • CM Abelian varieties and Shimura curves,(with D. Ramakrishnan), in preparation.
  • Twisted averages of L-functions, (with B. Ramakrishnan and M. Manickam), in preparation.
Books
  • Introduction to Abelian varieties, CRM Monograph Series Volume 3, Amer. Math. Soc., Providence, 1993. (112 pages).
  • Seminar on Fermat's Last Theorem , ed. K. Murty, CMS Conf. Proc. vol. 17, AMS, 1995. (265 pages)
  • Non-vanishing of L-functions and applications (with M. Ram Murty), Progress in Math. 157, Birkhauser, Basel, 1997. (196 pages)
  • Number Theory, ed. V. Kumar Murty and M. Waldschmidt, Contemporary Mathematics 210, Amer. Math. Soc., Providence, 1998. (399 pages)
  • Computational aspects of Number theory, (with S. Ali Miri), Preliminary Version.