Comparative Prime Number Theory Symposium

The "Comparative Prime Number Theory" symposium is a one-week event taking place on the main UBC campus in Vancouver, B.C., Canada from June 17–21, 2024.

Comparative prime number theory certainly includes prime number races, both classical races (Chebyshev's bias) and races associated with elliptic curves, number fields, and function fields. It also broadly includes the distribution of zeros of L-functions associated with these prime counting functions, including topics related to the Linear Independence hypothesis (LI) on the imaginary parts of those zeros, as well as general oscillations of number-theoretic error terms.

This symposium brings together established and early-career researchers with expertise and interest in comparative prime number theory to discuss various aspects of the current research. The purpose of this event is to highlight the recent advances in this area and initiate discussions and collaborations among researchers. We aim to provide a collaborative and supportive research environment for young researchers and an opportunity for established researchers to give mentorship and exchange ideas.

This symposium is the last major event of the PIMS Collaborative Research Group "L-functions in Analytic Number Theory". The plenary speakers will be:

  • Alexandre Bailleul (Université Paris–Saclay)
  • Lucile Devin (Université du Littoral Côte d’Opale)
  • Daniel Fiorilli (Université Paris–Saclay)
  • Florent Jouve (Université de Bordeaux)
  • Youness Lamzouri (Université de Lorraine)
  • Wanlin Li (Washington University in St. Louis)
Title Speaker Datesort descending
Fake mu's: Make Abstracts Great Again! Tim Trudgian June 17, 2024 - 9:30am
The Shanks–Rényi prime number race problem Youness Lamzouri June 17, 2024 - 10:30am
Prime Number Error Terms Nathan Ng June 17, 2024 - 11:30am
Joint distribution of central values and orders of Sha groups of quadratic twists of an elliptic curve Peng-Jie Wong June 17, 2024 - 3:30pm
The distribution of analytic ranks of elliptic curve over prime cyclic number fields Gyeongwon Oh June 17, 2024 - 4:00pm
Modular forms and an explicit Chebotarev variant of the Brun–Titchmarsh theorem Hari Iyer June 17, 2024 - 4:30pm
Remarks on Landau–Siegel zeros Debmalya Basak June 18, 2024 - 10:30am
The influence of the Galois group structure on the Chebyshev bias in number fields Mounir Hayani June 18, 2024 - 10:30am
Oscillations in Mertens’ product theorem for number fields Ethan Lee June 18, 2024 - 11:00am
A Mertens function analogue for the Rankin–Selberg L-function Amrinder Kaur June 18, 2024 - 11:30am
Counting “supersingularity” in arithmetic statistics Wanlin Li June 18, 2024 - 1:30pm
Explicit estimates for the Mertens function Nicol Leong June 18, 2024 - 2:30pm
Joint Distribution of primes in multiple short intervals Sun Kai Leung June 18, 2024 - 3:30pm
Quantitative upper bounds related to an isogeny criterion for elliptic curves Tian Wang June 18, 2024 - 4:00pm
Distribution of Gaussian primes and zeros of L-functions Lucile Devin June 19, 2024 - 9:00am
Shifting the ordinates of zeros of the Riemann zeta function William Banks June 19, 2024 - 11:00am
A simple proof of the Wiener–Ikehara Tauberian theorem Jagannath Sahoo June 19, 2024 - 11:30am
The Riemann hypothesis via the generalized von Mangoldt function Saloni Sinha June 20, 2024 - 9:30am
Moments in the Chebotarev density theorem Florent Jouve June 20, 2024 - 1:30pm
Average value of $\pi(t) - li(t)$ Daniel Johnston June 20, 2024 - 2:30pm
On the generalised Dirichlet divisor problem Chiara Bellotti June 20, 2024 - 3:30pm
Oscillation results for the summatory functions of fake \mu Chi Hoi (Kyle) Yip June 20, 2024 - 4:30pm
Unconditional comparative prime number theory over function fields Alexandre Bailleul June 21, 2024 - 9:00am
Spacing statistics of the Farey sequence Bittu June 21, 2024 - 10:30am
Zero-free regions of the Riemann zeta-function Andrew Yang June 21, 2024 - 1:30pm
Number theory versus random matrix theory: the joint moments story Andrew Pearce-Crump June 21, 2024 - 2:00pm
Ramanujan sums and the Hardy–Littlewood prime tuple conjecture Shivani Goel June 21, 2024 - 2:30pm
A race problem arising from elliptic curves Kin Ming Tsang June 21, 2024 - 3:30pm
Almost periodicity and large oscillations of prime counting functions Jan-Christoph Schlage-Puchta June 21, 2024 - 4:00pm