Скачать с ютуб Philippe Michel: Mixed moments for Dirichlet L-functions (NTWS 216) в хорошем качестве

Philippe Michel: Mixed moments for Dirichlet L-functions (NTWS 216)

In this talk we discuss the problem of evaluating somewhat exotic moments of Dirichlet L-functions of large modulus (called « mixed »). Namely moments of the shape $$\sum_{\chi(q)} L(\chi^{a_1},1/2)\cdots L(\chi^a_k,1/2)$$ where $q$ is a growing prime and $a_i,\ 1\leq i\leq k$ are fixed integers (that are not necessarily equal nor equal to $\pm 1$). We will discuss some partial results focusing mainly on the case $k=2$ and $3$. The techniques involved are non trivial bounds for solutions to monomial congruences equations as well as for averages of hyper-Kloosterman sums in short intervals. This is joint work with E. Fouvry, E. Kowalski and W. Sawin. Link to slides: https://drive.google.com/file/d/1DPFY... Number Theory Web Seminar: https://www.ntwebseminar.org Original air date: Thursday, June 13, 2024 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST) Friday, June 14, 2024 (1am AEST, 3am NZST)