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: Wanlin Li
A Dirichlet character over Fq(t) corresponds to a curve over Fq. Using this connection to geometry, we construct families of characters whose L-functions vanish (resp. does not vanish) at the central point. The existence of infinitely many vanishing...
Scientific, Seminar
ULethbridge Number Theory and Combinatorics Seminar: Alexandra Florea
I will talk about recent work towards a conjecture of Gonek regarding negative shifted moments of the Riemann zeta-function. I will explain how to obtain asymptotic formulas when the shift in the Riemann zeta function is big enough, and how we can...
Scientific, Seminar
ULethbridge Number Theory and Combinatorics Seminar: Julie Desjardins
The blow up of the anticanonical base point on X, a del Pezzo surface of degree 1, gives rise to a rational elliptic surface E with only irreducible fibers. The sections of minimal height of E are in correspondence with the 240 exceptional curves on...
Scientific, Seminar
Lethbridge Number Theory and Combinatorics Seminar: Elchin Hasanalizade
The Fibonacci sequence \(F(n) : (n\geq 0) is the binary recurrence sequence defined by $$ F(0) = F(1) = 1 \qquad \mbox{and} \\ F(n+2) = F(n+1) + F(n) \qquad \forall n \geq 0. $$ There is a broad literature on the Diophantine equations involving the...
Scientific, Seminar
PIMS CRG Seminar Series: L-functions in Analytic Number Theory: Xiannan Li
The behavior of quadratic twists of modular L-functions at the critical point is related both to coefficients of half integer weight modular forms and data on elliptic curves. Here we describe a proof of an asymptotic for the second moment of this...
Scientific, Seminar
PIMS CRG Seminar Series: L-functions in Analytic Number Theory: Shashank Chorge
We compute extreme values of the Riemann Zeta function at the critical points of the zeta function in the critical strip. i.e. the points where ζ′(s)=0 and Rs1. We show that the values taken by the zeta function at these points are very similar to...
Scientific, Seminar
PIMS CRG Seminar Series: L-functions in Analytic Number Theory: Chung Hang (Kevin) Kwan
In the past century, the studies of moments of L-functions have been important in number theory and are well-motivated by a variety of arithmetic applications. This talk will begin with two problems in elementary number theory, followed by a survey...