
Date Time 
Location  Speaker 
Title – click for abstract 

09/17 3:00pm 
BLOC 220 
Oguz Gezmis Texas A&M University 
Taelman Lvalues for Drinfeld modules over Tate algebras
In 2012, Pellarin defined an Lseries which can be seen as a
deformation of Goss's Lseries. In order to give new identities for
Pellarin LSeries, Anglès, Pellarin and Tavares Ribeiro introduced
Drinfeld modules over Tate algebras and also generalized the theory of
Taelman for Drinfeld modules of rank 1 over Tate algebras. Later on,
Anglès and Tavares Ribeiro expanded the theory for the special type of
Drinfeld modules of arbitrary rank over Tate algebras. In this talk, we
investigate Taelman Lvalues corresponding to Drinfeld modules over Tate
algebras of arbitrary rank. Using our results, we also introduce an
Lseries which can be seen as a generalization of Pellarin Lseries. 

09/24 3:00pm 
BLOC 220 
Naser Talebizadeh Sardari University of Wisconsin 
Bounds on the multiplicity of the Hecke eigenvalues
Fix an integer N and a prime p\nmid N where p> 3. Given any padic valuation v_p on \bar{\mathbb{Q}} (normalized with v_p(p)=1) and an algebraic integer \lambda \in \bar{\mathbb{Q}}; e.g., \lambda=0, we show that the number of newforms f of level N and even weight k such that T_p(f)=\lambda f is bounded independently of k and only depends on v_p(\lambda) and N. Abstract 

10/08 3:00pm 
BLOC 624 
Guchao Zeng Texas A&M University at Qatar 
vadic limits of BernoulliCarlitz numbers
The BernoulliCarlitz numbers BC_m for the rational function field K over a finite field of order q do not behave the same as the classical Bernoulli numbers. We show that BC_m has vadic limits (v is a finite place of K of degree d) for m of the form aq^{dj}+b, where a and b are positive integers. Moreover, the limit is in a constant field extension of K and invariant under the permutation of distance d. Joint work with M. Papanikolas. Abstract 

10/15 3:00pm 
BLOC 624 
Matt Young Texas A&M University 
The Weyl bound for Dirichlet Lfunctions
The problem of estimating central values of Lfunctions has attracted a
great deal of attention for many decades. The case of Dirichlet
Lfunctions, which one might expect to be one of the simpler families of
Lfunctions, has turned out to be unexpectedly difficult. In the 1960's,
Burgess proved a nontrivial bound that has only been improved in some
special cases. Notably, Conrey and Iwaniec obtained an improvement in the
case that the Dirichlet character is realvalued. I will discuss a
similarquality improvement valid for any Dirichlet character of cubefree
conductor. This is joint work with Ian Petrow.
Abstract 

10/22 3:00pm 
BLOC 220 
Changningphaabi Namoijam Texas A&M University 
Hyperderivatives of periods and quasiperiods of tmodules
Brownawell and Denis constructed, as extensions of Drinfeld modules by additive groups, divided derivatives of a Drinfeld module whose periods can be expressed in terms of hyperderivatives of the periods and quasiperiods of the given Drinfeld module. In this talk, we discuss how to obtain hyperderivatives of periods and quasiperiods of an abelian Anderson tmodule as periods and quasiperiods of the tmodule given by the minimal quasiperiodic extension of Maurischat's prolongation tmodule of the given tmodule. We also determine how periods, quasi periods, logarithms and quasilogarithms of an abelian Anderson tmodule appear as evaluations of solutions of Frobenius difference equations. This is joint work with Matt Papanikolas. Abstract 

11/19 3:00pm 
BLOC 624 
Jiakun Pan Texas A&M University 
Equidistribution of Eisenstein series in the level aspect
(Joint work with Matthew P. Young) We study Eisenstein series E^q(z,s) of weight zero, level q and primitive central character mod q, attached to cusp infinity, and for s fixed on the central line. As a result, we find that Quantum Unique Ergodicity holds for all large q unconditionally, for almost all primitive central characters to the modulus. Our research extends previous work of Kowalski, Michel, and Michel, Holowinsky and Soundararajan, Nelson, Pitale, and Saha, and etc. Abstract 

12/03 11:00am 
BLOC 220 
Madeline Locus Dawsey Emory University 
Densities of subsets of prime numbers
Thanks to the Prime Number Theorem, a lot is known about the distribution of prime numbers. In particular, one can ask whether the methods from analytic number theory yield formulas for densities of subsets of prime numbers. One famous instance of this is the strong form of Dirichlet's famous theorem on primes in arithmetic progressions. Here, we give new formulations of Dirichlet's Theorem, and more generally the Chebotarev Density Theorem, by offering completely new formulas expressing densities of suitable subsets of prime numbers. Our work can be thought of as the nonabelian extension of a theorem of Alladi from the 1970s. Abstract 