One-day workshop on Arithmetic Statistics

Room 108, Graduate School of Science Bldg. No. 3, Kyoto University (No. 5 on the North Campus Map)

* This workshop will take place on the day after the RIMS Workshop "Analytic Number Theory and Related Topics 2026".

• Linghu Fan (Kavli IPMU, The University of Tokyo)

• Masahiro Mine (Waseda University)

• Anders Södergren  (Chalmers University of Technology)

• Takehiko Yasuda (The University of Osaka)

October 17 (Saturday)

• 9:30–10:30 Masahiro Mine

• 11:00–12:00 Linghu Fan

• 13:30–14:30 Takehiko Yasuda

• 15:00–16:00 Anders Södergren

• Masahiro Mine (Waseda University)

  • Title: Statistical behavior of the Riemann zeta-function

  • Abstract: The study of the statistical behavior of the Riemann zeta-function was pioneered by Bohr and his collaborators in the early 20th century. The subject of this study is to investigate the density of the values of Riemann zeta-function on vertical lines belonging to a fixed set on the complex plane. Bohr and Jessen determined such a density for the case where the real part of the vertical line is greater than 1/2. However, the determination of the density remains unresolved in the case where the real part of the vertical line is equal to 1/2, that is, precisely on the critical line. In this talk, after providing an overview of previous research, I will introduce an approach using hyperfunctions as a new method for understanding the statistical behavior of the Riemann zeta-function on the critical line.

• Linghu Fan (Kavli IPMU, The University of Tokyo)

  • Title: Stringy Euler characteristic of modular quotient singularities

  • Abstract: Stringy Euler characteristic is an important geometric invariant in the study of the McKay correspondence. Consider the quotient singularity given by a finite subgroup of the special linear group. Over the complex numbers, it is known that the stringy Euler characteristic of the quotient equals the number of isomorphism classes of the irreducible representations of the finite group. In positive characteristic, Yasuda's wild McKay correspondence provides an approach to understand the stringy Euler characteristic via a counting problem of extensions of local fields, where the behaviours in modular cases are dramatically different from those over the complex numbers. In this talk, I will give a quick introduction of the McKay correspondence, and then introduce some results on the stringy Euler characteristic that are done in an arithmetic way.

• Takehiko Yasuda (The University of Osaka)

  • Title: The stacky Batyrev-Manin conjecture and its extension to wild stacks

  • Abstract: The Batyrev–Manin conjecture predicts the asymptotic distribution of rational points of bounded height on algebraic varieties. Malle's conjecture, on the other hand, predicts the distribution of finite extensions of a global field ordered by discriminant. These two apparently different conjectures can be viewed in a common framework by considering rational points on algebraic stacks.

In joint work with Ratko Darda, we formulated a stacky version of the Batyrev–Manin conjecture. In this framework, geometric invariants associated with twisted sectors enter the definition of heights and the expected asymptotic formula, and Malle's conjecture appears as a special case for classifying stacks.

I will then discuss an extension of this picture to positive characteristic. When stabilizer groups have order divisible by the characteristic, the stack is wild, and twisted sectors are no longer sufficient to capture the relevant geometry. We replace them by more general objects called sectoroids and introduce a corresponding class of height functions. This framework includes discriminant heights of torsors.

Finally, I will discuss joint work with Darda on counting torsors for finite abelian p-groups over global fields of characteristic p. For a broad class of heights, we obtain asymptotic formulas of the form predicted by the wild stacky Batyrev–Manin conjecture.

• Anders Södergren  (Chalmers University of Technology)

  • Title: 

  • Abstract: