Publications

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Algebraic Geometry

  • The Manin-Drinfeld theorem and Ramanujan suma

    with Ramakrishnan, D.
    Proc. Indian Acad. Sci. 97 (1988) 251-262
  • The Albanese variety of a unitary Shimura variety

    with Ramakrishnan, D.
    The Zeta Functions of Picard Modular Surfaces, ed. R. Langlands, D Ramakrishnan, CRM (1992) 445-464
  • Period relations and Tate's conjecture for Hilbert modular surfaces

    with Ramakrishnan, D.
    Inventiones Math 89 (1987) 319-345
  • Semiregularity and Abelian varieties


    Special volume in honour of S Bloch, Fields Institute Communications, Volume 56, American Math Society, Providence (2009) 293-305
  • Exceptional Hodge classes on certain abelian varieties


    Math. Annalen, 268 (1984) 197-206
  • The Hodge group of an abelian variety


    Proc. Amer. Math. Soc. 104 (1) (1988) 61-68
  • Algebraic cycles on abelian varieties


    Duke Math J. 50 (1983) 487-504
  • Hodge and Weil classes on Abelian varieties


    The Arithmetic and Geometry of Algebraic Cycles, eds B. Gordon, J. Lewis and N. Yui, Kluwer Academic Publishers, Amsterdam (2000) 83-115
  • Tate cycles on a product of two Hilbert modular sutface

    with Prasad, D.
    J Number Theory, 80 (2000) 25-43
  • Computing the Hodge group of an Abelian variety


    Seminaire de theorie de Nombres Paris, ed. C Goldstein, Birkhauser-Verlag (1990) 141-158
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    Algebraic Number Theory

  • Distribution of values of $\frac{L'}{L} (\sigma, \chi_D)$

    with Mourtada, M.
    Moscow Math J. (to appear) (2013)
  • Bounded and finite generation of arithmetic groups


    CMS Conf. Proc., vol. 15, Number theory, ed. K. Dilcher, AMS (1995) 249-261
  • The field of Fourier coefficients of a modular form


    Ramanujan Mathematical Society Volume in Honour of T. C. Vasudevan, RMS, Chennai (2011) 103-111
  • Frobenius distributions and Galois representations


    Proc. Symp. Pure Math., vol 66, part 1, Automorphic Forms, Automorphic Representations and Arithmetic, ed. R. Doran, Z-L. Dou, G. Gilbert, Amer. Math. Soc., Providence (1999) 193-211
  • Modular forms and the Chebotarev Density Theorem, II


    Analytic Number Theory, ed. Y. Motohashi, London Math. Soc. Lecture Notes 247, Cambridge Univ. Press (1997) 287-308
  • Class numbers of CM fields with solvable normal closure


    Compositio Math, 127 (2001) 273-287
  • A Tauberian estimate for sums of coefficients of Dirichlet series


    Comptes Rendus Math. Rep. Acad. Sci. Canada, 21 (1999) 153-159
  • Splitting of primes in infinite extensions


    Proceedings of the Millenial Conference on Number Theory, eds. A. Hildebrand, B. Berndt and N. Boston, A.K. Peters, Boston (2001) 23-41
  • The fundamental group of the reductive Borel-Serre and Satake compactifications

    with Ji, L., Saper, L., and Scherk, J.
    Asian J. Math., 19 (2015) 465-486
  • Stark zeros in certain towers of fields


    Math Res. Letters, 6 (1999) 511-520
  • Modular forms and the Chebotarev density theorem

    with Murty, Ram M., and Saradha, N.
    Amer. Journal of Math. 110 (1988) 253-281
  • The least prime in a conjugacy class


    Comptes Rendus Math. Rep. Acad. Sci. Canada, 22(4) (2000) 129-146
  • The Euclidean algorithm for $S$-integers

    with Murty, Ram M., and Gupta, R.
    CMS Conference Proceedings 7 (1987) 189-201
  • The growth of the Selmer group of an elliptic curve with split multiplicative reduction

    with Lim, M. Fai
    Intl J Number Theory, 10 (2014) 675-687
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    Analytic Number Theory

  • An analogue of the Siegel Walfisz theorem for the cyclicity of CM elliptic curves mod p

    with Akbary, A.
    Indian J Pure Appl Math, 41 (2010) 25-37
  • Ramanujan and prime numbers


    The Legacy of Srinivasa Ramanujan, eds. B Berndt and D Prasad, RMS Lecture Notes 20, Ramanujan Mathematical Society, Chennai (2013) 281-299
  • The least prime which does not split completely


    Forum Mathematicum, 6 (1994) 555-565
  • The Euler-Kronecker constant of a cyclotomic field


    Annales des Sciences Mathematiques du Quebec, 35 (2011) 239-247
  • Average Values of quadratic twists of modular $L$-functions

    with Stefanicki, T.
    Func. et. Approx., 28 (2000) 155-172
  • Some results in number theory, II


    Number theory, eds. S Adhikari, R Balasubramanian, K Srinivas, Ramanujan Math. Soc. Lecture Notes, 1 (2005) 51-55
  • On the logarithmic derivatives of Dirichlet L functions at s=1

    with Ihara, Y., and Shimura, M.
    Acta Arithmetica, 137 (2009) 253-276
  • Holomorphy of Artin $L$-functions


    Proc. Intl. Conf. on Ramanujan, Ramanujan Mathematical Society (1989) 11-24
  • Mean values of derivatives of modular $L$-functions

    with Murty, Ram M.
    Annals of Math. 133 (1991) 447-475
  • Zeros of Dirichlet $L$-functions

    with Balasubramanian, R.
    Ann. Scient. Ecole Norm. Sup., 25 (1992) 567-615
  • The Lindelof class of L functions


    The conference on L functions, eds L Weng and M Kaneko, World Scientific (2007) 165-174
  • Some results in number theory I

    with Murty, Ram M.
    Acta Arith. 35 (1979) 367-371
  • A variant of Lehmer's conjecture


    J Number Theory, 123 (2007) 80-91
  • Non-vanishing of $L$-functions and their derivatives


    Proc. Montreal Conf. on modular forms, ed. R. Murty, Univ of Montreal Press (1990) 89-113
  • On a conjecture of Lang and Trotter

    with Akbary, A., and Ghioca, D.
    Math Annalen, 347 (2010) 365-394
  • A variant of Lehmer's conjecture II: The CM case

    with Gun, S.
    Canadian J Math, 63 (2011) 298-326
  • A variant of the Lang-Trotter conjecture

    with Murty, Ram M.
    Number Theory, Analysis and Geometry: In memory of Serge Lang, eds. D Ramakrishnan et. al., Springer (2011) 461-474
  • Transcendental values of class group L-functions

    with Murty, Ram M.
    Math Annalen, 351 (2011) 835-855
  • Omega theorems for $\frac{L'}{L} (1, \chi_D)$

    with Mourtada, M.
    Intl J Number Theory, 9 (2013) 561-581
  • Zeros and poles of Artin $L$-functions

    with Foote, R.
    Math. Proc. Camb. Phil. Soc. 105 (1989) 5-11
  • On the Sato-Tate conjecture II


    On Certain L-functions: A Volume in honour of F. Shahidi, Clay Mathematics Proceedings 43, Amer. Math. Soc., Providence (2011) 471-482
  • A variant of the Bombieri Vinogradov theorem

    with Murty, Ram M.
    CMS Conference proceedings, 7 (1987) 243-272
  • Strong multiplicity one for Selberg's Class

    with Murty, Ram M.
    C.R. Acad. Sci., 319, Paris (1994) 315-320
  • An examination of identity management models in an internet setting

    with Giuliani, K.
    Cyber Security, Cyber Crime and Cyber Forensics: Applications and Perspectives eds. R. Santanam, M. Sethumadhavan, M. Virendra, IGI Global Press, Pennsylvania (2011) 106-114
  • Explicit formulae and the Lang-Trotter conjecture


    Rocky Mountain J. Math. 15 (2) (1985) 535-551
  • The Sato-Tate conjecture and generalizations

    with Murty, Ram M.
    Current Trends in Science: Platinum Jubilee Special of the Indian Academy of Sciences, ed. N. Mukunda, Indian Academy of Sciences, Bangalore (2009) 639-646
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    Arithmetic Geometry

  • An analogue of the Siegel Walfisz theorem for the cyclicity of CM elliptic curves mod p

    with Akbary, A.
    Indian J Pure Appl Math, 41 (2010) 25-37
  • A growth of Selmer ranks of an Abelian variety with complex multiplication

    with Ouyang, Y.
    Pure and Appl Math Quarterly, 2 (2006) 539-555
  • Tate cycles on Abelian varieties with complex multiplication

    with Patankar, V.
    Canadian J. Math., 67 (2015) 198-213
  • Growth of Selmer groups of CM Abelian varieties

    with Lim, M. Fai
    Canadian J. Math, 67 (2015) 654-666
  • Effective versions of the Chebotarev density theorem for function fields

    with Scherk, J.
    C.R. Acad. Sci., 319, Paris (1994) 523-528
  • On the Sato-Tate conjecture


    Number Theory related to Fermat's last Theorem, ed. N. Koblitz, Birkhauser-Verlag, Boston (1982) 195-205
  • Splitting of Abelian varieties: a new local global problem


    Algebra and Number Theory, ed. R. Tandon, Hindustan Book Agency, New Dehli (2005) 258-268
  • Modular elliptic curves


    CMS Conf. Proc. vol. 17, Seminar on Fermat's Last Theorem, ed. K. Murty, AMS (1995) 1-38
  • Descending rational points on elliptic curves to smaller fields

    with Akbary, A.
    Canadian J. Math., 53 (2001) 449-469
  • Splitting of Abelian varieties

    with Patankar, V.
    Intl Math Res Not, article ID rnn033, doi: 10.1093/imrn /rnn033 (2008) 27 pages
  • Base change and the Birch and Swinnerton-Dyer conjecture

    with Murty, Ram M.
    Contemporary Math., 143 (Papers in Honor of E. Grosswald), ed. M. Knopp (1993) 481-494
  • Splitting of Abelian varieties II: Elliptic Dynkin Pairs

    with Zong, Y.
    (submitted) (2014)
  • Reduction mod p of subgroups of the Mordell Weil group of an elliptic curve

    with Akbary, A.
    Intl J Number Theory, 5 (2009) 1-23
  • An examination of identity management models in an internet setting

    with Giuliani, K.
    Cyber Security, Cyber Crime and Cyber Forensics: Applications and Perspectives eds. R. Santanam, M. Sethumadhavan, M. Virendra, IGI Global Press, Pennsylvania (2011) 106-114
  • The growth of the Selmer group of an elliptic curve with split multiplicative reduction

    with Lim, M. Fai
    Intl J Number Theory, 10 (2014) 675-687
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    Automorphic Forms

  • Lacunarity and modular forms


    J. Indian Math. Soc., 57 (1988) 127-146
  • The field of Fourier coefficients of a modular form


    Ramanujan Mathematical Society Volume in Honour of T. C. Vasudevan, RMS, Chennai (2011) 103-111
  • Prime divisors of Fourier coefficients of modular forms

    with Murty, Ram M.
    Duke Math. J. 51 (1984) 57-77
  • An analogue of the Erdos-Kac theorem for Fourier coefficients of modular forms

    with Murty, Ram M.
    Indian J. Pure and Appl. Math. 15 (10) (1984) 1090-1101
  • Estimates for sums of coefficients of Dirichlet series with functional equation


    The Ramanujan Journal, 7 (2003) 225-235
  • Odd values of the Ramanujan $\tau$ Function

    with Murty, Ram M., and Shorey, T.N.
    Bulletin Math. Soc. France 115 (1987) 391-395
  • Fourier coefficients of forms of CM type

    with Laptyeva, N.
    Indian J. Pure Appl. Math., 45 (2014) 747-758
  • On a conjecture of Lang and Trotter

    with Akbary, A., and Ghioca, D.
    Math Annalen, 347 (2010) 365-394
  • A variant of Lehmer's conjecture II: The CM case

    with Gun, S.
    Canadian J Math, 63 (2011) 298-326
  • A variant of the Lang-Trotter conjecture

    with Murty, Ram M.
    Number Theory, Analysis and Geometry: In memory of Serge Lang, eds. D Ramakrishnan et. al., Springer (2011) 461-474
  • On the Sato-Tate conjecture II


    On Certain L-functions: A Volume in honour of F. Shahidi, Clay Mathematics Proceedings 43, Amer. Math. Soc., Providence (2011) 471-482
  • The Sato-Tate conjecture and generalizations

    with Murty, Ram M.
    Current Trends in Science: Platinum Jubilee Special of the Indian Academy of Sciences, ed. N. Mukunda, Indian Academy of Sciences, Bangalore (2009) 639-646
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    Cryptography

  • A privacy preserving e-payment architecture

    with Plateaux, A., Coquet, V., Vernois, S., Lacharme, P., and Rosenberger, C.
    Lecture Notes in Computer Science, 7859, Springer-Verlag, Heidelberg (2013) 402
  • Online user's registration respecting privacy

    with Plateaux, A., Lacharme, P., and Rosenberger, C.
    International Conference on Mobile Applications and Security Management, DOI: 10.1109/WCCIT.2013.6618718, IEEE, 2013 (2013) 1-5
  • Cryptosystems arising from Abelian varieties


    Handbook of Finite Fields, eds. G. Mullen and D. Panario, CRC Press, Boca Raton (2013) 803-811
  • Security and authentication for networked storage

    with Xu, G.
    SECRYPT, eds. E. Fernandez Medina et. al., INSTICC Press, Portugal (2008) 477-480
  • ERINDALE: A polynomial based hashing algorithm

    with Volkovs, N.
    Lecture Notes in Computer Science 5557, Springer Verlag, Berlin, International Workshop on Coding and Cryptographyeds. eds. C Xing et al (2009) 157-170
  • An e-payment architecture ensuring a high level of privacy protection

    with Plateaux, A., Lacharme, P., Coquet, V., Vernois, S., and Rosenberger, C.
    Security and Privacy in Communication Networks, Lecture Notes of the Institute for Computer Science, Social Informatics and Telecommunications Engineering, 127 (2013) 305-322
  • Nonadjacent radix tau expansions of integers in Euclidean imaginary quadratic number fields

    with Blake, I., and Xu, G.
    Canadian J Math, 60 (2008) 1267-1282
  • Non linear secret sharing and prime numbers

    with Xu, G.
    Discrete Mathematics and Applications, ed. M Sethumadhavan, Narosa Publishing, Chennai (2005) 1-10
  • Efficient algorithms for Koblitz curves over fields of characteristics three

    with Blake, I., and Xu, G.
    J. Discrete Algorithms (2005) 113-124
  • An application of sieve methods to elliptic curves

    with Ali Miri, S.
    Lecture Notes in Computer Science 2247, INDOCRYPT 2001, eds. C. Pandu Rangan, C. Ding, Springer Verlag, Berlin (2001) 91-98
  • Refinements of Millers algorithms for computing the Weil Tate pairing

    with Blake, I., and Xu, G.
    J. Algorithms (2006) 134-149
  • A polynomial based hashing algorithm

    with Volkovs, N.
    SECRYPT 2008 International Conference on Security and Cryptography, eds. E Fernandez Medina et. al. INSTICC Press, Portugal (2008) 103-106
  • Counting points on an Abelian variety over a finite field

    with Izadi, F.A.
    Lecture Notes in Computer Science 2904, INDOCRYPT 2003, eds. T Johansson, S Maitra, Springer-Verlag, Berlin (2004) 323-333
  • The addition law on hyperelliptic Jacobians


    Current Trends in Number Theory, eds. S Adhikari, S A Katre, B Ramakrishnan, Hindustan Book Agency, New Delhi (2002) 101-110
  • A contactless e-health information system with privacy

    with Plateaux, A., Lacharme, P., and Rosenberger, C.
    Wireless Communications and Mobile Computing Conference, DOI: 10.1109/IWCMC.2013.6583805, IEEE (2013) 1660-1665
  • A note on the Window $\tau$-NAF algorithm

    with Blake, I., and Xu, G.
    Information Processing Letters, 95 (2005) 496-502
  • Abelian varieties - optimal cryptography for wireless communications?


    Wireless Security Perspectives, 2 (2000) 3-5
  • Abelian varieties and cryptography in INDOCRYPT


    Lecture Notes in Computer Science, 3797, ed. C. Veni Madhavan (2005) 1-12
  • An examination of identity management models in an internet setting

    with Giuliani, K.
    Cyber Security, Cyber Crime and Cyber Forensics: Applications and Perspectives eds. R. Santanam, M. Sethumadhavan, M. Virendra, IGI Global Press, Pennsylvania (2011) 106-114
  • Algebraic curves and cryptography


    Fields Institute Communications 53, Amer. Math. Soc., Providence (2010) 133 pages
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    Expository

  • Ramanujan and Harish-Chandra


    Math. Intelligencer, 15 (1993) 33-39
  • The notion of a Shimura variety


    Advances in Number Theory, ed. F. Gouvea, N. Yui, Oxford University Press (1993) 195-212
  • Fermat's Last Theorem


    Analysis, Geometry and Probability, ed. R. Bhatia, Hindustan Book Agency, New Delhi (1996) 125-139
  • The work of Sarvadaman Chowla

    with Murty, Ram M., and Williams, K.S.
    The Collected Works of S Chowla, ed. J. Huard and K. Williams, CRM, Montreal (2000) 7-25
  • Report on Fermat's Last Theorem


    Current Sceience, 67 (2) (1994) 82-88
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    Group Theory

  • On the density of various classes of croups

    with Murty, Ram M.
    J. Number Theory 17 (1983) 29-36
  • On groups of squarefree order

    with Murty, Ram M.
    Math. Annalen 267 (1984) 1090-1101
  • On the enumeration of finite groups

    with Murty, Ram M., and Erdos, P.
    J. Number Theory 25 (1987) 360-378
  • The number of groups of a given order

    with Murty, Ram M.
    J. Number Theory 18 (1984) 178-191
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    Topology

  • The fundamental group of the reductive Borel-Serre and Satake compactifications

    with Ji, L., Saper, L., and Scherk, J.
    Asian J. Math., 19 (2015) 465-486
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    Transcendental Number Theory

  • On a conjecture of Shorey

    with Murty, Ram M.
    Diophanatine Equations, ed. N. Saradha, Narosa, New Delhi (2008) 167-176
  • Irrational numbers arising from certain differential equations

    with Murty, Ram M.
    Canadian Math. Bull. 20 (1977) 117-120
  • On a problem of Ruderman

    with Murty, Ram M.
    Amer. Math. Monthly, 118 (2011) 644-650
  • Transcendental values of class group L functions II

    with Murty, Ram M.
    Proc. Amer. Math. Soc., 140 (2012) 3041-3047
  • On transcendence of generalized Euler Lehmer constants II

    with Gun, S., and Saha, E.
    (2014)
  • Transcendental values of class group L-functions

    with Murty, Ram M.
    Math Annalen, 351 (2011) 835-855
  • A problem of Chowla revisited

    with Murty, Ram M.
    J Number Theory, 131 (2011) 1723-1733
  • Odd values of Fourier coefficients of certain modular forms

    with Murty, Ram M.
    Intl J Number Theory (2007) 455-470
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    Other

  • A note on diagonal and Hermitian hyper surfaces

    with Blake, I., and Use fi, H.
    submitted (2014)
  • Counting finite groups

    with Murty, Ram M.
    preprint (1983)
  • Splitting of Abelian varieties

    with Zong, Y.
    Advances in Mathematics of Communication, 8 (2014) 511-519
  • Heilbronn Characters

    with Foote, R., and Ginsburg, H.
    Bulletin of the Amer. Math. Soc., 52 (2015) 465-496

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