Comparative Prime Number Theory
Takeaways from the symposium
List of open problems
The CPNTS open problem list is now online.
In lieu of having a problem session during the symposium, we have created a list of open problems related to the theme of the symposium, including any of these topics:
classical prime-counting functions
races among primes in arithmetic progressions
races associated with elliptic curves, number fields, and function fields
summatory functions of arithmetic functions such as μ(n), (-1)^{Ω(n)}, τ(n), etc.
the distribution of zeros of L-functions associated with the above races, including the linear independence of their imaginary parts
general oscillations and frequency of sign changes of number-theoretic error terms.
The list will remain available afterwards on this symposium website.
Our hope is that this list will stimulate research and lead to future collaborations among symposium participants. In particular, problems on the list are intended to be available for anyone to decide to work on. We encourage you to contribute any open problems that you don't mind sharing, or problems that you're not actively working on (unless you are seeking collaborators). Each problem that is listed will have the name and affiliation of the submitter unless requested otherwise.
Lecture videos and slides
Alexandre Bailleul, Unconditional comparative prime number theory over function fields
William Banks, Shifting the ordinates of zeros of the Riemann zeta function
Debmalya Basak, Remarks on Landau–Siegel zeros
Chiara Bellotti, On the generalised Dirichlet divisor problem
Sneha Chaubey, Bias for the κ-factor function
Shashank Chorge, Voronoi summation formulas for the product of the generalized divisor function and the Liouville lambda function
Lucile Devin, Distribution of Gaussian primes and zeros of L-functions
Daniel Fiorilli, Moments of primes using comparative number theory tools
Shivani Goel, Ramanujan sums and the Hardy–Littlewood prime tuple conjecture
Mounir Hayani, The influence of the Galois group structure on the Chebyshev bias in number fields
Hari Iyer, Modular forms and an explicit Chebotarev variant of the Brun–Titchmarsh theorem
Daniel Johnston, The average value of π(t)–li(t)
Florent Jouve, Moments in the Chebotarev density theorem
Amrinder Kaur, A Mertens function analogue for the Rankin–Selberg L-function
Youness Lamzouri, The Shanks–Rényi prime number race problem
Ethan Lee, Oscillations in Mertens’ product theorem for number fields
Nicol Leong, Explicit estimates for the Mertens function
Sun Kai Leung, Joint distribution of primes in multiple short intervals
Wanlin Li, Counting “supersingularity” in arithmetic statistics
Nathan Ng, Prime number error terms
Gyeongwon Oh, The distribution of analytic ranks of elliptic curve over prime cyclic number fields
Andrew Pearce-Crump, Number theory versus random matrix theory: the joint moments story
Jagannath Sahoo, A simple proof of the Wiener–Ikehara Tauberian theorem
Jan-Christoph Schlage-Puchta, Almost periodicity and large oscillations of prime counting functions
Saloni Sinha, The Riemann hypothesis via the generalized von Mangoldt function
Tim Trudgian, Fake mu’s: Make Abstracts Great Again!
Kin Ming Tsang, A race problem arising from elliptic curves
Tian Wang, Quantitative upper bounds related to an isogeny criterion for elliptic curves
Peng-Jie Wong, Joint distribution of central values and orders of Sha groups of quadratic twists of an elliptic curve
Andrew Yang, Zero-free regions of the Riemann zeta-function
Chi Hoi (Kyle) Yip, Oscillation results for the summatory functions of fake μ’s
Annotated bibliography
In September 2023, a UBC team posted the first version of An annotated bibliography for comparative prime number theory on the arXiv. The goal of this annotated bibliography is to record every publication on the topic of comparative prime number theory together with a summary of its results, using a unified system of notation for the quantities being studied and for the hypotheses under which results are obtained.
Photos from the symposium
