Andrew Odlyzko: Papers on Zeros of the Riemann Zeta Function and Related Topics (see also "Tables of zeros of the zeta function" and "Some unpublished materials" on the main home page)

• Alan Turing and the Riemann zeta function, D. A. Hejhal and A. M. Odlyzko. in Alan Turing - His Work and Impact, S. Barry Cooper and Jan van Leeuwen, eds., Elsevier, 2013, pp. 265-279. [PDF]

• Numerical study of the derivative of the Riemann zeta function at zeros, G. A. Hiary and A. M. Odlyzko, Commentarii Mathematici Universitatis Sancti Pauli, vol. 60, no. 1-2, 2011, pp. 47-60. [PDF]

• The zeta function on the critical line: Numerical evidence for moments and random matrix theory models, G. A. Hiary and A. M. Odlyzko, Math. Comp., vol. 81, no. 279, July 2012, pp. 1723-1752. [preprint, PDF]

• The 10^22-nd zero of the Riemann zeta function, A. M. Odlyzko. Dynamical, Spectral, and Arithmetic Zeta Functions, M. van Frankenhuysen and M. L. Lapidus, eds., Amer. Math. Soc., Contemporary Math. series, no. 290, 2001, pp. 139-144. [Abstract] [PDF]

• An improved bound for the de Bruijn-Newman constant, A. M. Odlyzko, Numerical Algorithms, 25 (2000), pp. 293-303. [Abstract] [PDF]

• A nonlinear equation and its application to nearest neighbor spacings for zeros of the zeta function and eigenvalues of random matrices, P. J. Forrester and A. M. Odlyzko, in Organic Mathematics, J. Borwein, P. Borwein, L. Jorgenson, and R. Corless, eds., Amer. Math. Soc. 1997, pp. 239-250. Electronic version available at http://www.cecm.sfu.ca/projects/OMP/. [PDF] A condensed version, GUE eigenvalues and Riemann zeta function zeros: A non-linear equation for a new statistic has appeared in Phys. Rev. E 54 (1996), pp. R4493-R4495. [PDF]

• Short proofs for nondivisibility of sparse polynomials under the extended Riemann hypothesis, D. Yu. Grigoriev, M. Karpinski, and A. M. Odlyzko, Fund. Inform. 28 (1996), pp. 297-301. Preliminary version on pp. 117-122 in Proc. Intern. Symp. Symbolic Algebraic Computation: ISSAC '92, P. S. Wang (ed.), ACM Press, (1992). [PDF]

• Analytic computations in number theory, A. M. Odlyzko, Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics, W. Gautschi (ed.), Amer. Math. Soc., Proc. Symp. Appl. Math. #48 (1994), pp. 451-463. [PDF]

• A New Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant LAMBDA, G. Csordas, A. M. Odlyzko, W. Smith, and R. S. Varga, Electr. Trans. Num. Anal., 1 (1993), pp. 104-111. [PDF] [comments]

• Nonexistence of Siegel zeros in towers of radical extensions, A. M. Odlyzko, and C. M. Skinner, pp. 499-511 in A Tribute to Emil Grosswald: Number Theory and Related Analysis, M. Knopp and M. Sheingorn (eds.), American Math. Soc., Contemporary Math. #143 (1993). [PDF]

• Primes, quantum chaos, and computers, A. M. Odlyzko, pp. 35-46 in Number Theory, National Research Council (1990). [PDF]

• Bounds for discriminants and related estimates for class numbers, regulators, and zeros of zeta functions: A survey of recent results, A. M. Odlyzko, Sem. Theorie des Nombres, Bordeaux, 2 (1990), pp. 119-141. [online journal version] [preprint, PDF] [PDF of updated tables and references] [comments]

• Supercomputers and the Riemann zeta function, A. M. Odlyzko, pp. 348-352 in Supercomputing '89: Supercomputing Structures & Computations, Proc. 4-th Intern. Conf. on Supercomputing, L. P. Kartashev and S. I. Kartashev (eds.), Intern. Supercomputing Inst. (1989). [PDF]

• Fast algorithms for multiple evaluations of the Riemann zeta function, A. M. Odlyzko and A. Schoenhage, Trans. Am. Math. Soc., 309 (1988), pp. 797-809. [online journal version]

• Large deviations of sums of independent random variables, H. L. Montgomery and A. M. Odlyzko, Acta Arith., 49 (1988), pp. 427-434. [online journal version]

• New analytic algorithms in number theory, A. M. Odlyzko, pp. 466-475 in Proceedings 1986 International Congress of Mathematicians, Amer. Math. Soc., 1987, [PDF]

• On the distribution of spacings between zeros of the zeta function, A. M. Odlyzko, Math. Comp., 48 (1987), pp. 273-308. [online journal version]

• Computing pi(x): An analytic method, J. C. Lagarias and A. M. Odlyzko, J. Algorithms, 8 (1987), pp. 173-191. [PDF]

• Disproof of the Mertens conjecture, A. M. Odlyzko and H. J. J. te Riele, J. reine angew. Math., 357 (1985), pp. 138-160. [PDF]

• New algorithms for computing pi(x), J. C. Lagarias and A. M. Odlyzko, pp. 176-193 in Number Theory: New York 1982, D. V. Chudnovsky, G. V. Chudnovsky, H. Cohn and M. B. Nathanson (eds.), Springer-Verlag, Lecture Notes in Mathematics #1052, 1984.

• Gaps between zeros of the zeta function, H. L. Montgomery and A. M. Odlyzko, pp. 1079-1106 in Topics in Classical Number Theory: Coll. Math. Soc. Janos Bolyai 34., G. Halasz (ed.), North-Holland, 1984.

• On computing Artin L-functions in the critical strip, J. C. Lagarias and A. M. Odlyzko, Math. Comp., 33 (1979), pp. 1081-1095. [online journal version]

• A bound for the least prime ideal in the Chebotarev density theorem, J. C. Lagarias, H. L. Montgomery, and A. M. Odlyzko, Inventiones math., 54 (1979), pp. 271-296. [online journal version]

• On conductors and discriminants, A. M. Odlyzko, pp. 377-407 in Algebraic Number Fields, A. Frohlich (ed.), Academic Press, 1977.

• Lower bounds for discriminants of number fields II, A. M. Odlyzko, Tohoku Math. J., 29 (1977), pp. 209-216.

• Effective versions of the Chebotarev density theorem, J. C. Lagarias and A. M. Odlyzko, pp. 409-464 in Algebraic Number Fields, A. Frohlich (ed.), Academic Press, 1977.

• Lower bounds for discriminants of number fields, A. M. Odlyzko, Acta Arith., 29 (1976), pp. 275-297. [online journal version]

• Some analytic estimates of class numbers and discriminants, A. M. Odlyzko, Inventiones math., 29 (1975), pp. 275-286. [online journal version]