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: Henry Twiss
Subconvexity problems have maintained extreme interest in analytic number theory for decades. Critical barriers such as the convexity, Burgess, and Weyl bounds hold particular interest because one usually needs to drastically adjust the analytic...
Scientific, Seminar
L-functions in Analytic Number Theory: Martin Čech
There are two ways to compute moments in families of L-functions: one uses the approximation by Dirichlet polynomials, and the other is based on multiple Dirichlet series. We will introduce the two methods to study the family of real Dirichlet L...
Scientific, Seminar
L-functions in Analytic Number Theory: Saloni Sinha
We study sums of the form ∑n≤x f(n) n⁻ⁱʸ, where f is an arithmetic function, and we establish an equivalence between the Riemann Hypothesis and estimates on these sums. In this talk, we will explore examples of such sums with specific arithmetic...
Scientific, Seminar
L-functions in Analytic Number Theory: Christine K. Chang
We will present a matching upper and lower bound for the right tail probability of the maximum of a random model of the Riemann zeta function over short intervals. In particular, we show that the right tail interpolates between that of log-correlated...
Scientific, Seminar
L-functions in Analytic Number Theory: Andrew Yang
A zero-free region of the Riemann zeta-function is a subset of the complex plane where the zeta-function is known to not vanish. In this talk we will discuss various computational and analytic techniques used to enlarge the zero-free region for the...
Scientific, Seminar
L-functions in Analytic Number Theory: Andrés Chirre
In this talk, we will discuss a well-known formula of Ramanujan and its relationship with the partial sums of the Möbius function. Under some conjectures, we analyze a finer structure of the involved terms. It is a joint work with Steven M. Gonek...
Scientific, Seminar
L-functions in Analytic Number Theory: Greg Knapp
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
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
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
CANCELLED: L-functions in Analytic Number Theory: Sneha Chaubey
The topic on the distribution of sequences saw its light with the seminal paper of Weyl. While the classical notion of equidistribution modulo one addresses the “global” behaviour of the fractional parts of a sequence, quantities such as k-point...