Events and Activities

Since work of Montgomery and Katz-Sarnak, the eigenvalues of random matrices have been used to model the zeroes of the Riemann zeta function and other L-functions. Keating and Snaith extended this to also model the distribution of values of the L...

We'll discuss problems where bounds for L-functions have arisen as inputs and where techniques for estimating them through their integral representations have been useful (all of which have been shaped and influenced by Peter Sarnak’s work).

Bounds for Dirichlet polynomials play an important role in several questions connected to the distribution of primes. For example, they can be used to bound the number of zeroes of the Riemann zeta function in vertical strips, which is relevant to...

Bounds for Dirichlet polynomials play an important role in several questions connected to the distribution of primes. For example, they can be used to bound the number of zeroes of the Riemann zeta function in vertical strips, which is relevant to...

Abstract: The Mobius function is one of the most important arithmetic functions. There is a vague yet well known principle regarding its randomness properties called the “Mobius randomness law". It basically states that the Mobius function should be...

Abstract: The Higher order Fourier uniformity conjecture asserts that on most short intervals, the Mobius function is asymptotically uniform in the sense of Gowers; in particular, its normalized Fourier coefficients decay to zero.  This conjecture...

Abstract: Cohen, Lenstra, and Martinet have given highly influential conjectures on the distribution of class groups of number fields, the finite abelian groups that control the factorization in number fields. Malle, using tabulation of class groups...

Abstract: Starting with the "Leibniz" formula for $\pi$

$ \pi/4 = 1 - 1/3 + 1/5 - 1/7 + \ldots$

the special values of Dirichlet L-functions have long been a source of fascination and frustration. From Euler's solution in 1734 of the Basel problem to...