L-Functions in Analytic Number Theory
Analytic number theory focuses on arithmetic questions through the lens of L-functions. These generating series encode arithmetic information and have connections with a host of other mathematical fields, such as algebraic number theory, harmonic analysis, Diophantine approximation, probability, representation theory, and computational number theory. The main focuses of this CRG include moments of L-functions and automorphic forms, explicit results in analytic number theory, and comparative prime number theory.
Scientific, Seminar
L-functions in Analytic Number Theory: Julia Stadlmann
The twin prime conjecture asserts that there are infinitely many primes p for which p+2 is also prime. This conjecture appears far out of reach of current mathematical techniques. However, in 2013 Zhang achieved a breakthrough, showing that there...
Scientific, Seminar
L-functions in Analytic Number Theory: Biitu
Scientific, Seminar
L-functions in Analytic Number Theory: Vivian Kuperberg
In 2000, Shiu proved that there are infinitely many primes whose last digit is 1 such that the next prime also ends in a 1. However, it is an open problem to show that there are infinitely many primes ending in 1 such that the next prime ends in 3...
Scientific, Seminar
L-functions in Analytic Number Theory: Emily Quesada-Herrera
We will explore how a Fourier optimization framework may be used to study two classical problems in number theory involving Dirichlet characters: The problem of estimating the least character non-residue; and the problem of estimating the least prime...
Scientific, Seminar
L-functions in Analytic Number Theory: Winston Heap
We discuss the role of long Dirichlet polynomials in number theory. We first survey some applications of mean values of long Dirichlet polynomials over primes in the theory of the Riemann zeta function which includes central limit theorems and pair...
Scientific, Seminar
L-functions in Analytic Number Theory: Chiara Bellotti
In this talk, we prove that |ζ(σ+it)|≤ 70.7 |t|4.438(1-σ)^{3/2} log2/3|t| for 1/2≤ σ ≤ 1 and |t| ≥ 3, combining new explicit bounds for the Vinogradov integral with exponential sum estimates. As a consequence, we improve the explicit zero-free region...
Seminar
L-functions in Analytic Number Theory: Siegfred Baluyot
In the late 90's, Keating and Snaith used random matrix theory to predict the exact leading terms of conjectural asymptotic formulas for all integral moments of the Riemann zeta-function. Prior to their work, no number-theoretic argument or heuristic...
Scientific, Seminar
L-functions in Analytic Number Theory: Andrew Pearce-Crump
In the 1960s Shanks conjectured that the $\zeta(\rho)$, where $\rho$ is a non-trivial zero of zeta, is both real and positive in the mean. Conjecturing and proving this result has a rich history, but efforts to generalise it to higher moments have so...
Scientific, Seminar
L-functions in Analytic Number Theory: Shivani Goel
The Hardy and Littlewood k-tuple prime conjecture is one of the most enduring unsolved problems in mathematics. In 1999, Gadiyar and Padma presented a heuristic derivation of the 2-tuples conjecture by employing the orthogonality principle of...
Scientific, Seminar
L-functions in Analytic Number Theory: Lucile Devin
Generalizing the original Chebyshev bias can go in many directions: one can adapt the setting to virtually any equidistribution result encoded by a finite number of L-functions. In this talk, we will discuss what happens when one needs an infinite...