Nancy-Metz number theory seminar - Institut Élie Cartan de Lorraine

Upcoming presentations

Exponential sums with random multiplicative coefficients

Catégorie d'évènement : Séminaire de Théorie des Nombres de Nancy-Metz Date/heure : 20 March 2025 14:30-15:30 Lieu : Salle Döblin Oratrice ou orateur : Seth Hardy (University of Warwick) Résumé :

Random multiplicative functions are random models for arithmetic functions such as Dirichlet characters. Moments of sums involving random multiplicative functions are related to interesting counting problems, and understanding these counts can allow one to deduce the limiting distribution of the sums. Using this idea, Benatar, Nishry, and Rodgers showed that the limiting distribution of exponential sums with random multiplicative coefficients is Gaussian. However, they found that moments do not suffice if one wishes to understand the maximum size of these exponential sums. After introducing random multiplicative functions, we will discuss why this is the case, and show how one can obtain conjecturally sharp lower bounds for the maximum size of exponential sums with random multiplicative coefficients.

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Upcoming presentations

Exponential sums with random multiplicative coefficients

Résolution du problème d'approximation par dilatations de Erdős

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Past presentations

Tilings for beta-numeration

Differentiability of fractional integrals of modular forms and Brjuno functions

La conjecture galoisienne de Brumer-Stark

Fonctions complètement multiplicatives de somme nulle

Abscissae of functions related to a class of problems of analytic number theory

Metric Diophantine approximation on manifolds

Sums of primes and powers of a fixed positve integer

Prime number races with very many competitors

Divisibility by 16 of class numbers in certain families of quadratic number fields

Sommes d'exponentielles courtes et entiers sans facteur carré