L-Functions in Analytic Number Theory

A Collaborative Research Group (CRG) typically consists of researchers with a common research interest and with a common desire to collaboratively develop some aspects of their research programs. The groups may already exist, organizing joint seminars and workshops, making joint PDF appointments, or developing joint graduate training programs, but will have the potential to do much more, given resources and organizational structure through PIMS.
Every year, the PIMS Scientific Review Panel (SRP) will select, on a competitive basis, from the proposals, several areas of research. CRGs are generally developed with the advice of PIMS starting with a letter of intent accepted by the SRP. More details are available at http://pims.math.ca/scientific/call-proposals. Proposals can vary greatly according to the needs of the particular group and may combine a number of existing PIMS activities.

Further information on PIMS CRG activities can be found on the PIMS website (CRG).

Title Date Speaker
Almost periodicity and large oscillations of prime counting functions Jun 21, 2024 Jan-Christoph Schlage-Puchta
A race problem arising from elliptic curves Jun 21, 2024 Kin Ming Tsang
Ramanujan sums and the Hardy–Littlewood prime tuple conjecture Jun 21, 2024 Shivani Goel
Number theory versus random matrix theory: the joint moments story Jun 21, 2024 Andrew Pearce-Crump
Zero-free regions of the Riemann zeta-function Jun 21, 2024 Andrew Yang
Spacing statistics of the Farey sequence Jun 21, 2024 Bittu
Unconditional comparative prime number theory over function fields Jun 21, 2024 Alexandre Bailleul
Oscillation results for the summatory functions of fake \mu Jun 20, 2024 Chi Hoi (Kyle) Yip
On the generalised Dirichlet divisor problem Jun 20, 2024 Chiara Bellotti
Average value of $\pi(t) - li(t)$ Jun 20, 2024 Daniel Johnston
Moments in the Chebotarev density theorem Jun 20, 2024 Florent Jouve
The Riemann hypothesis via the generalized von Mangoldt function Jun 20, 2024 Saloni Sinha
A simple proof of the Wiener–Ikehara Tauberian theorem Jun 19, 2024 Jagannath Sahoo
Shifting the ordinates of zeros of the Riemann zeta function Jun 19, 2024 William Banks
Distribution of Gaussian primes and zeros of L-functions Jun 19, 2024 Lucile Devin
Quantitative upper bounds related to an isogeny criterion for elliptic curves Jun 18, 2024 Tian Wang
Joint Distribution of primes in multiple short intervals Jun 18, 2024 Sun Kai Leung
Explicit estimates for the Mertens function Jun 18, 2024 Nicol Leong
Counting “supersingularity” in arithmetic statistics Jun 18, 2024 Wanlin Li
A Mertens function analogue for the Rankin–Selberg L-function Jun 18, 2024 Amrinder Kaur
Oscillations in Mertens’ product theorem for number fields Jun 18, 2024 Ethan Lee
Remarks on Landau–Siegel zeros Jun 18, 2024 Debmalya Basak
The influence of the Galois group structure on the Chebyshev bias in number fields Jun 18, 2024 Mounir Hayani
Modular forms and an explicit Chebotarev variant of the Brun–Titchmarsh theorem Jun 17, 2024 Hari Iyer
The distribution of analytic ranks of elliptic curve over prime cyclic number fields Jun 17, 2024 Gyeongwon Oh
Joint distribution of central values and orders of Sha groups of quadratic twists of an elliptic curve Jun 17, 2024 Peng-Jie Wong
Bias for the kappa factor function Jun 17, 2024 Sneha Chaubey
Prime Number Error Terms Jun 17, 2024 Nathan Ng
The Shanks–Rényi prime number race problem Jun 17, 2024 Youness Lamzouri
Fake mu's: Make Abstracts Great Again! Jun 17, 2024 Tim Trudgian
Bounds on the Number of Solutions to Thue Equations Apr 10, 2024 Greg Knapp
Zeros of linear combinations of Dirichlet L-functions on the critical line Mar 25, 2024 Jérémy Dousselin
Zeros of linear combinations of Dirichlet L-functions on the critical line Mar 25, 2024 Jérémy Dousselin
The fourth moment of quadratic Dirichlet L-functions Mar 18, 2024 to Apr 18, 2024 Quanli Shen
Primes in arithmetic progressions to smooth moduli Mar 4, 2024 Julia Stadlmann
L-functions in Analytic Number Theory: Biitu Feb 26, 2024 Bittu
Consecutive sums of two squares in arithmetic progressions Feb 9, 2024 Vivian Kuperberg
Fourier optimization and the least quadratic non-residue Jan 29, 2024 Emily Quesada-Herrera
Mean values of long Dirichlet polynomials Jan 22, 2024 Winston Heap
Explicit bounds for $\zeta$ and a new zero free region Jan 16, 2024 Chiara Bellotti
Möbius function, an identity factory with applications Dec 4, 2023 Sebastian Zuniga Alterman
Twisted moments of characteristic polynomials of random matrices Nov 27, 2023 Siegfred Baluyot
Characteristic polynomials, the Hybrid model, and the Ratios Conjecture Nov 20, 2023 Andrew Pearce-Crump
The eighth moment of $\Gamma_1(q)$ L-functions Nov 6, 2023 Vorrapan Chandee
On the Hardy Littlewood 3-tuple prime conjecture and convolutions of Ramanujan sums Oct 30, 2023 Shivani Goel
Conditional estimates for logarithms and logarithmic derivatives in the Selberg class Oct 16, 2023 Neea Palojärvi
An explicit estimate on the mean value of the error in the prime number theorem in intervals Oct 3, 2023 Michaela Cully-Hugill
Sign changes of the error term in the Piltz divisor problem Sep 25, 2023 Cruz Castillo
The second moment of symmetric square L-functions over Gaussian integers Apr 5, 2023 Olga Balkanova
Exceptional Chebyshev's bias over finite fields Mar 22, 2023 Alexandre Bailleul
Euler's divergent series and primes in arithmetic progressions Mar 8, 2023 Anne-Maria Ernvall-Hytönen
A new explicit bound for the Riemann zeta function Mar 1, 2023 Ghaith Hiary
A logarithmic improvement in the Bombieri-Vinogradov theorem Feb 8, 2023 Alisa Sedunova
An explicit error term in the prime number theorem for large x Jan 25, 2023 Daniel Johnston
Least quadratic non-residue and related problems Jan 18, 2023 Enrique Treviño
Zeros of linear combinations of L-functions near the critical line Jan 11, 2023 Youness Lamzouri
A walk on Legendre paths Jan 9, 2023 Youness Lamzouri
Negative moments of the Riemann zeta-function Dec 5, 2022 Alexandra Florea
The value distribution of the Hurwitz zeta function with an irrational shift Dec 1, 2022 Anurag Sahay
Quadratic Twists of Modular L-functions Nov 3, 2022 Xiannan Li
Moments and Periods for GL(3) Oct 20, 2022 Chung-Hang (Kevin) Kwan
Extreme Values of the Riemann Zeta Function and Dirichlet L-functions at the Critical Points of the Zeta Function Oct 13, 2022 Shashank Chorge
Multiplicative functions in short intervals Oct 6, 2022 Paranedu Darbar
Joint value distribution of L-functions Sep 22, 2022 Junxian Li
Moments of the Hurwitz zeta function Jul 29, 2022 Anurag Sahay
An extension of Venkatesh's converse theorem to the Selberg class Jul 29, 2022 Min Lee
Averages of long Dirichlet polynomials with modular coefficients Jul 29, 2022 Alessandro Fazzari
Local statistics for zeros of Artin--Schreier $L$-functions Jul 29, 2022 Alexei Entin
Moments of $L$-functions in the world of number field counting Jul 29, 2022 Brandon Alberts
The eighth moment of the Riemann zeta function Jul 29, 2022 Quanli Shen
Geodesic restrictions of Maass forms and moments of Hecke $L$-functions Jul 28, 2022 Peter Humphries
Twisted first moment of $GL(3)\times GL(2)$ $L$-function Jul 28, 2022 Jakob Streipel
Double square moments and bounds for resonance sums for cusp forms Jul 28, 2022 Praneel Samanta
$L^p$-norm bounds for automorphic forms Jul 28, 2022 Rizwanur Khan
Moments of large families of Dirichlet $L$-functions Jul 27, 2022 Vorrapan Chandee
Discrete Moments Jul 27, 2022 Fatma Cicek
Quantum variance for automorphic forms Jul 27, 2022 Bingrong Huang,
Logging of the zeta-function, but only for a few moments! Jul 26, 2022 Tim Trudgian
The third moment of quadratic $L$-Functions Jul 26, 2022 Ian Whitehead
Asymptotic mean square of product of higher derivatives of the zeta-function and Dirichlet polynomials Jul 26, 2022 Mithun Das
Lambert series of logarithm and a mean value theorem for $\zeta(\frac{1}{2}-it)\zeta'(\frac{1}{2}+it)$ Jul 26, 2022 Atul Dixit
Negative moments of the Riemann zeta function Jul 25, 2022 Alexandra Florea
The recipe for moments of $L$-functions Jul 25, 2022 Siegfried Baluyot
The generalised Shanks's conjecture Jul 25, 2022 to Jul 26, 2022 Andrew Pearce-Crump
One-level density of zeros of Dirichlet L-functions over function fields Jul 25, 2022 Hua Lin
Distributions of sums of the divisor function over function fields Jul 25, 2022 Matilde Lalín
Selberg's central limit theorem for quadratic Dirichlet $L$-functions over function fields Jul 25, 2022 Allysa Lumley