Séminaire de Théorie des Nombres de Nancy-Metz - Institut Élie Cartan de Lorraine

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The distribution of random polynomials with multiplicative coefficients

Catégorie d'évènement : Analyse et théorie des nombres Date/heure : 18 février 2021 14:30-15:30 Lieu : Oratrice ou orateur : Brad Rodgers Résumé :

A classic paper of Salem and Zygmund investigates the distribution of trigonometric polynomials whose coefficients are chosen randomly (say +1 or -1 with equal probability) and independently. Salem and Zygmund characterized the typical distribution of such polynomials (gaussian) and the typical magnitude of their sup-norms (a degree N polynomial typically has sup-norm of size $\sqrt{N \log N}$ for large N). In this talk we will explore what happens when a weak dependence is introduced between coefficients of the polynomials; namely we consider polynomials with coefficients given by random multiplicative functions. We consider analogues of Salem and Zygmund’s results, exploring similarities and some differences.

Special attention will be given to a beautiful point-counting argument introduced by Vaughan and Wooley which ends up being useful.

This is joint work with Jacques Benatar and Alon Nishry.

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Exposés à venir

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The distribution of random polynomials with multiplicative coefficients

Non-vanishing of cubic L-functions

Comportement aléatoire local des suites réelles: résultats métriques, énergie additive et inégalités diophantiennes

Théorèmes d'Erdös-Wintner effectifs

Sur la répartition jointe de la représentation d'Ostrowski dans les classes de résidus

Soutenance de thèse : Lois gaussiennes inverses généralisées, lois de Kummer et méthode de Stein

Automatic multiplicative sequences

Local-Global Principle for integers from thin subgroups of $SL_2(mathbb{Z}[i])$

On the classification of completely multiplicative automatic sequences

Irregularities of Dirichlet L-functions and a Chebyshev-type bias for zeros