There will be talks in October and November 2025. The seminar will take place in Aula INdAM at 12.
2025.10.17. Cathy Swaenepoel (Université Paris Cité)
Prime numbers with an almost prime reverse
Let b>1 be an integer. For any non-negative integer n, we call reverse of n in base b the integer obtained by reversing the digits of n. The existence of infinitely many prime numbers whose reverse is also prime is an open problem. In this talk, we will present a joint work with Cécile Dartyge and Joël Rivat, in which we show that there are infinitely many primes with an almost prime reverse. More precisely, we show that there exist an explicit positive integer Ω_b and a real number c_b>0 such that, for at least c_b*b^λ/λ² primes p ∈ [ b^{λ-1} , b^λ [, the reverse of p has at most Ω_b prime factors. Our proof is based on sieve methods and on obtaining a result in the spirit of the Bombieri-Vinogradov theorem concerning the distribution in arithmetic progressions of the reverse of prime numbers.
2025.11.21. Alberto Perelli (Università di Genova)
Funzioni L: una panoramica sulla classe di Selberg
La classe di Selberg è un modello analitico assiomatico per le funzioni L; la panoramica presenterà le congetture e i risultati principali, in particolare relativi ai twist non-lineari e alle loro applicazioni.
2025.11.28. Morten Risager (University of Copenhagen)
[This talk will be in Sala di Consiglio at 12:00]
The error term in the hyperbolic circle problem
We survey various known bounds on the error term in the hyperbolic circle problem. We then go on to explain how we may obtain a new logarithmic saving on Selberg’s pointwise bound in the case of the full modular group, and specific Heegner points related to different squarefree fundamental discriminants. This is joint work with Dimitrios Chatzakos, Giacomo Cherubini, and Stephen Lester.
2026.02.25. Paola Chilla (University of Heidelberg)
[Note the different day and time! This talk will be on Wednesday February 25, 2026, at 9h30.]
Towards a Jacquet-Langlands correspondence for function field modular forms
The Jacquet-Langlands correspondence relates modular forms for GL2 and for its inner forms, i.e. for unit groups of quaternion algebras, and was historically the first known example of Langlands transfer. It is natural to ask whether a similar correspondence holds in the realm of function fields. While the original analytic proof does not adapt to this setting, a geometric approach, based on étale cohomology computations, proves more fruitful. In this talk, I will discuss a first step towards a Jacquet-Langlands correspondence for function field modular forms. For a definite quaternion algebra ramified at exactly one finite place, I will associate Hecke eigensystems of rank 2 Drinfeld cusp forms to those arising from functions on quaternionic adèlic double quotients. The resulting Drinfeld cusp forms are new at the ramified prime, in the sense of Bandini and Valentino. The talk is based on the speaker’s PhD thesis, written under the supervision of Prof. Gebhard Böckle.
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