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: Vorrapan Chandee
In this talk, I will discuss my on-going joint work with Xiannan Li on an unconditional asymptotic formula for the eighth moment of Γ1(q) L-functions, which are associated with eigenforms for the congruence subgroups Γ1(q). Similar to a large family...
Scientific, Seminar
L-functions in Analytic Number Theory: Neea Palojärvi
The Selberg class consists of functions sharing similar properties to the Riemann zeta function. The Riemann zeta function is one example of the functions in this class. The estimates for logarithms of Selberg class functions and their logarithmic...
Scientific, Seminar
L-functions in Analytic Number Theory: Cruz Castillo
For an integer k≥3; Δk (x) :=∑n≤xdk(n)-Ress=1 (ζk(s)xs/s), where dk(n) is the k-fold divisor function, and ζ(s) is the Riemann zeta-function. In the 1950's, Tong showed for all large enough X; Δk(x) changes sign at least once in the interval [X, X +...
Scientific, Seminar
L-functions in Analytic Number Theory: Vorrapan Chandee
In this talk, I will discuss my on-going joint work with Xiannan Li on an unconditional asymptotic formula for the eighth moment of Γ1(q) L-functions, which are associated with eigenforms for the congruence subgroups Γ1(q). Similar to a large family...
Scientific, Conference
Comparative Prime Number Theory Symposium
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: Olga Balkanova
We prove an explicit formula for the first moment of Maass form symmetric square L-functions defined over Gaussian integers. As a consequence, we derive a new upper bound for the second moment. This is joint work with Dmitry Frolenkov.
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...