January 31, 2025 at TU Graz

Location: Steyrergasse 30, HS BE01

Schedule: 

13:30-14:30:  Sam Chow (University of Warwick)

Title: Smooth discrepancy and Littlewood’s conjecture 

Abstract: We establish a deterministic analogue of Beck’s local-to-global principle for Kronecker sequences. This gives rise to a novel reformulation of Littlewood’s conjecture in diophantine approximation.

14:30-15:00: Tea break

15:00-16:00: Matteo Verzobio (ISTA)

Title: On the L-polynomials of curves over finite fields 

Abstract: Let q be a prime power and g ≥ 1. Consider a smooth projective curve C of genus g defined over the finite field Fq​. We introduce the L-polynomial associated with C. Additionally, we examine the distribution of the coefficients of L-polynomials in the family of curves with genus g.

16:00-16:15: Break

16:15-17:15:  Andrei Shubin (TU Graz)

Title: Prime number theorem for sums of digits in several bases 

Abstract: In 1967, Gelfond established an asymptotic formula for the sum of digits of an integer n in base q in arithmetic progressions. He posted a few questions about the distribution of sums of digits along subsequences, such primes and integer polynomials. The formula for primes was established by Mauduit and Rivat, and later Drmota, Mauduit, and Rivat extended this result to two different bases simultaneously.

I will talk about the proof for any number of bases. This is a joint work with Clemens Müllner and Lukas Spiegelhofer

18:00: Dinner