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 Seminar: Sumaia Saad Eddin
The values of Dirichlet L-functions at s=1 have long attracted considerable attention due to their deep algebraic and geometric significance. In contrast, the logarithmic derivatives of Dirichlet L-functions at s=1, which play a key role in the study...
Scientific, Seminar
L-functions in Analytic Number Theory Seminar: Antonio Pedro Ramos
TBA
Scientific, Seminar
L-functions in Analytic Number Theory Seminar: Kübra Benli
Deuring-Heilbronnn phenomenon, quantitatively established by Linnik in 1944, describes how the existence of a Landau-Siegel zero, which is real and near s=1, affects the location of the rest of the zeros of the Dirichlet L-functions to the same...
Scientific, Seminar
L-functions in Analytic Number Theory Seminar: Sun Kai Leung
The higher-order Titchmarsh problem concerns the correlation between higher divisor functions and primes. In this talk, I will explain how to derive an asymptotic formula for this correlation in appropriate ranges, assuming the existence of a "strong...
Scientific, Seminar
L-functions in Analytic Number Theory Seminar: Arshay Sheth
Even though Euler products of L-functions are generally valid only to the right of the critical strip, there is a strong sense in which they should persist even inside the critical strip. Indeed, the behaviour of Euler products inside the critical...
Scientific, Seminar
L-functions in Analytic Number Theory Seminar: Kübra Benli
TBA
Scientific, Seminar
L-functions in Analytic Number Theory Seminar: Nicol Leong
Bounds on the logarithmic derivative and the reciprocal of the Riemann zeta function are studied as they have a wide range of applications, such as computing bounds for Mertens function. In this talk, we are mainly concerned with explicit bounds...
Scientific, Seminar
L-functions in Analytic Number Theory Seminar: Valeriya Kovaleva
In this talk we will discuss the behaviour of the Riemann zeta on the critical line, and in particular, its correlations in various ranges. We will prove a new result for correlations of squares, where shifts may be up to size T3/2-ε. We will also...
Scientific, Seminar
L-functions in Analytic Number Theory: Jackie Voros
The least quadratic non-residue has been a central problem in number theory for centuries. The average least quadratic non-residue was explored by Erdős in the 1960s, and many extensions of this problem such as to the average least character non...
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...