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Iwaniec, W. Luo, P. Sarnak , Low lying zeros of families of L -functions, I. Jacquet, J. Shalika , On Euler products and the classification of automorphic representations I, Amer. Jacquet, I. Piatetski-Shapiro, J. Shalika , Rankin-Selberg convolutions, Amer.

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Katz, P. Keating, N. Kim, P.

Research projects

Sarnak , Refined estimates towards the Ramanujan and Selberg conjectures, preprint, Kim, F. Kneser , Darstelungsmasse indefiniter quadratische Formen, Math. Kolyvagin, D.

Ram Murty 1/8 Partial summation formula and applications

Lugachev , Finiteness of the Shafarevich-Tate group and the group of rational points for some modular abelian varieties, Leningrad Math. Kowalski, P. Michel, J.

Vanderkam , Rankin-Selberg L -functions in the level aspect, preprint, Vanderkam , Nonvanishing of high derivatives of automorphic L -functions at the center of the critical strip, J. SB ,— Langlands , Problems in the theory of automorphic forms, S. Linnik , Dokl. Nauk SSSR 30 , — Linnik , Additive problems and eigenvalues of the modular operators, Proc.

ICM Stockholm , — Linnik , Ergodic properties of algebraic fields, Ergebnisse, 45 Springer Verlag Luo , Nonvanishing of L -values and the strong Weyl law, preprint, Luo, Z.

Advanced Analytic Number Theory: L-Functions

Rudnick, P. Pure Math. Merel , Bornes pour la torsion de courbes elliptiques sur les corps de nombres, Invent. I, Budapest Colloq. Michel , Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman.

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I, Invent. Montgomery , The pair-correlation of zeros of the zeta function, Proc.

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Odlyzko , The 10 20 -th zero of the Riemann zeta function and 70 million of its neighbors, preprint, A. Petersson , Zur analytischeu theorie de grenzkreisgruppen, Math. Phillips, P. Rubinstein , Evidence for a spectral interpretation of zeros of L -functions, , thesis, Princeton. Rudnick , Letter to Peter Sarnak Sarnak , Zeros of principle L -functions and random matrix theory, Duke Math.

Research projects

Sarnak , The behavior of eigenstates of arithmetic hyperbolic manifolds, CMP , — Satake , Spherical functions and the Ramanujan conjecture, Proc. Satake , Theory of spherical functions on reductive algebraic groups over p -adic fields, Publ. IHES 18 Some specific funded projects are listed below, but many of our students instead arrive at a project through discussion with potential supervisors.

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Research projects Find a postgraduate research project in your area of interest by exploring the research projects we offer in the Department of Mathematics. Javascript is required to view PhD Opportunities. Modular Integrals and Their Mellin Transforms. The Coefficients of Cyclotomic Polynomials. Best Possible Results on the Density of Sumsets. Some Powers of The Euler Product. Diagonalizing Eisenstein Series. Some Binary Partition Functions. On the Minimal Level of Modular Forms.

Back Matter Pages About this book Introduction On April , , over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. For fifteen of these years, he served as head of the mathematics department. Delange, P. Erdos, H. Iwaniec, M.