The Ohio State University Number Theory Seminar Mondays 4:30 pm MW 154 (building photo) W. Sinnott, D. Goss, J. Cogdell R. Holowinsky, W. Luo

 Scheduled Talks 04/23/2013 - Guillaume Ricotta (Bordeaux) - Fourier coefficients of GL(3) automorphic forms in arithmetic progressions (abstract) We prove that the Fourier coefficients of GL(3) Hecke-Maass cusp forms in arithmetic progression modulo a prime number p have a Gaussian limit distribution as p goes to infinity. This is a joint work with Emmanuel Kowalski. Availability Calendar

 If you would like to give a talk at the OSU Number Theory Seminar, please check the calendar below for available dates and send an e-mail to holowinsky.1 (at) osu.edu for possible scheduling.

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 Past Talks 2012-2013 04/08/2013 - Craig Franze (OSU) - An asymptotic expansion related to the Dickman function. (abstract) 04/01/2013 - Joachim Schwermer (Vienna) - On Lefschetz numbers and arithmetically defined hyperbolic 3-manifolds. (abstract) 02/25/2013 - Bruce Berndt (UIUC) - Unpublished Manuscripts Published with Ramanujan's Lost Notebook. (abstract) 02/04/2013 - Youness Lamzouri (York U) - Large Character Sums. (abstract) 01/14/2013 - Dimitris Koukoulopoulos (Montreal) - When the sieve works. (abstract) 12/03/2012 - Ghaith Hiary (Bristol) - Computing Dirichlet $L$-functions.(abstract) 11/19/2012 - Kevin Ford (UIUC) - Sets $S$ of primes with $p$ in $S$ and $q|(p-1)$ implying $q$ in $S$. (abstract) 10/22/2012 - Micah Milinovich (Ole Miss) - Simple zeros of L-functions of modular forms. (abstract) 10/01/2012 - Tim All (OSU) - On p-adic annihilators of real ideal classes. (abstract) 09/24/2012 - David Goss (OSU) - From Carlitz's module to Euler's Gamma function. (abstract) 09/17/2012 - Roman Holowinsky (OSU) - Hybrid Subconvexity Bounds for Rankin-Selberg Convolutions. (abstract) We will consider various moment averages over special values of Rankin-Selberg convolution $L$-functions $L(\frac{1}{2}, \pi_1 \times \pi_2)$. Each $\pi_j$ will contribute to the size of the associated analytic conductor and we shall take advantage of this fact in order to obtain hybrid subconvexity bounds for individual $L$-values. Topics presented here will be a combination of ongoing joint projects with Nicolas Templier and Ritabrata Munshi. 09/10/2012 - Jim Cogdell (OSU) - The local Langlands correspondence for GL(n) and the symmetric and exterior square $\varepsilon$-factors (abstract) 2011-2012 05/21/2012 - Sun Kim (OSU) - Bessel function series and the circle and divisor problems. (abstract) In approximately 1915, Ramanujan recorded without proofs two identities involving doubly infinite series of Bessel functions. The two identities are connected with the classical circle and divisor problems, respectively. For each of Ramanujan's identities, there are three possible interpretations for the double series. The first identity was proved under those three and the second identity was proved under two of them. In this talk, we briefly review some key aspects of the proofs. Furthermore, we discuss trigonometric analogues of the identities, and a generalization of the first identity in the setting of Riesz sums. This is joint work with Bruce Berndt and Alexandru Zaharescu. 04/30/2012 - Ben Brubaker (MIT) - Demazure operators and Iwahori Whittaker functions. (abstract) Around 1980, Casselman and Shalika gave an elegant proof of a formula (conjectured by Langlands) for the spherical Whittaker function of an unramified principal series. We will begin by reviewing these terms and some key aspects of the proof, which relies on clever manipulations in the Iwahori-Hecke algebra. Then we explore similar formulas for Iwahori-fixed vectors in the unramified principal series, where we "rediscover" a Hecke algebra action due to Lusztig, in the context of equivariant K-theory. (This is joint work with Dan Bump and Tony Licata). 04/23/2012 - Hourong Qin (Nanjing) - The Local $L$-series of CM Elliptic Curves and Quadratic Polynomials Represent Primes. (abstract) Let $E$ be an elliptic curve defined over $\mathbb{Q}$ with complex multiplication. Fix an integer $r$. We give sufficient and necessary conditions for $a_p=r$ for some prime $p$. We show that there are infinitely many primes $p$ such that $a_p=r$ for some fixed integer $r$ if and only if a quadratic polynomial represents infinitely many primes $p$. In particular, for $E: y^2=x^3+x$, our result inplies that there are infinitely many primes $p$ such that $a_p=2$ if and only if there are infinitely many primes $p$ of the form $n^2+1$. 04/16/2012 - Peng Zhao (Princeton) - The Quantum Variance of PSL(2,Z)\PSL(2,R). (abstract) We discuss the quantum variance, which is introduced by Zelditch and describes the fluctuations of a quantum observable, on the phase space of modular surface. We asymptotically evaluate the quantum variance and show that it is equal to the classical variance of the geodesic flow on the phase space after inserting the "correction factor" of certain L-function's central value on each irreducible subspace. It is also very close to the arithmetic variance studied by Luo, Rudnick and Sarnak. This talk is based on a joint work with Peter Sarnak. 03/12/2012 - Henry Kim (Toronto) - Application of the strong Artin conjecture to the class number problem. (abstract) 02/09/2012 - Guillaume Ricotta (Bordeaux) - Height of Heegner points. (abstract) 12/05/2011 - Nathan Conrad Jones (University of Mississippi) - An alternative view of primitivity of Dirichlet characters. (abstract) 10/18/2011 (1:30 pm) - Amy DeCelles (Goshen) - Number theoretic applications of the automorphic spectral theory of higher rank groups. (abstract) 10/10/2011 - Federico Pellarin (St. Etienne) - On the values of certain L-series at even" positive integers. (abstract) 10/03/2011 - Kenneth Ward (Oklahoma State) - An asymptotic relation of class number and genus for abelian extensions of a function field. (abstract) 09/19/2011 - Abhishek Saha (ETH) - Determination of modular forms by Fourier coefficients. (abstract) 2010-2011 05/16/2011 - Sheng-Chi Liu (Texas A&M) - The L^2 restriction norms of Satio-Kurokawa lifts. (abstract) 05/09/2011 - Solomon Friedberg (Boston College) - Eisenstein series, crystals and ice. (abstract) 05/02/2011 - Ling Long (Iowa State) - Recent developments on modular forms for noncongruence subgroups. (abstract) 02/28/2011 - Jeff Hoffstein (Brown) - Shifted multiple Dirichlet series and moments of L-series. (abstract) 02/21/2011 - Gautam Chinta (CUNY) - Orthogonal periods of Eisenstein series. (abstract) 12/03/2010 - Noam Elkies (Harvard) - On the areas of rational triangles. (abstract) 11/22/2010 - Aaron Levin (Michigan State) - Runge's effective method for integral points. (abstract) 11/16/2010 - Lenny Taelman (Leiden) - The Carlitz sheaf, cyclotomic function fields, and Vandiver's conjecture. (abstract) 11/15/2010 - Xiaoqing Li (SUNY Buffalo) - The L^2 restriction of a GL(3) Maass form to GL(2). (abstract) 11/08/2010 - Paul Nelson (Caltech) - Equidistribution of cusp forms in the level aspect. (abstract) 11/01/2010 - Eddie Herman (AIM) - Beyond Endoscopy for the Asai L-function and Quadratic Base Change.(abstract) 10/25/2010 - David Goss (OSU) - The class number formula of Lenny Taelman. (abstract) 10/18/2010 - Jim Cogdell (OSU) - On Local L-functions. (abstract) 10/11/2010 - Yangbo Ye (Iowa) - Resonance of automorphic forms for GL(2) and GL(3). (abstract) 10/04/2010 - Timothy All (OSU) - Mihailescu's Theorem (formerly Catalan's conjecture); an outline of the proof.(abstract) More Number Theory

Mailing

Roman Holowinsky
Department of Mathematics
The Ohio State University
100 Math Tower
231 West 18th Avenue
Columbus, OH 43210-1174

http://www.math.ohio-state.edu

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