L-Functions in Analytic Number Theory

2022 2025

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, Conference
Comparative Prime Number Theory Symposium
June 17–21, 2024
University of British Columbia
The “Comparative Prime Number Theory” symposium is one of the highlight events organized by the PIMS-funded Collaborative Research Group (CRG) “ L-functions in Analytic Number Theory”. It is a one-week event taking place on the UBC campus in...
Scientific, Seminar
L-functions in Analytic Number Theory: Greg Knapp
April 10, 2024
University of Lethbridge
In 1909, Thue proved that when $F(x,y)$ is an irreducible, homogeneous, polynomial with integer coefficients and degree at least 3, the inequality $\left\| F(x,y) \right\| \leq h$ has finitely many integer-pair solutions for any positive $h$. Because...
Scientific, Seminar
L-functions in Analytic Number Theory: Jérémy Dousselin
March 25, 2024
University of Lethbridge
Fix $N\geq 1$ and let $L_1, L_2, \ldots, L_N$ be Dirichlet L-functions with distinct, primitive and even Dirichlet characters. We assume that these functions satisfy the same functional equation. Let $F(s)∶= c_1L_1(s)+c_2L_2(s)+\ldots+c_NL_N(s)$ be a...
Scientific, Seminar
L-functions in Analytic Number Theory: Quanli Shen
March 18, 2024
University of Lethbridge
I will discuss the fourth moment of quadratic Dirichlet L-functions where we prove an asymptotic formula with four main terms unconditionally. Previously, the asymptotic formula was established with the leading main term under generalized Riemann...
Scientific, Seminar
L-functions in Analytic Number Theory: Julia Stadlmann
March 4, 2024
University of Lethbridge
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: Vivian Kuperberg
February 12, 2024
University of Lethbridge
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
January 29, 2024
University of Lethbridge
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
January 22, 2024
University of Lethbridge
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
January 16, 2024
University of Lethbridge
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...
PIMS Site Director - University of Lethbridge
University of British Columbia
University of Lethbridge
University of Northern British Columbia