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: drive.google.com/file/d/1DPFY...
Number Theory Web Seminar: 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)