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Number Theory Seminar

Thursday, January 25, 2024
2:30pm to 3:30pm
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Linde Hall 255
Toroidal cubic moment for Dirichlet L-functions
Philippe Michel, Ecole Polytechnique Federale de Lausanne,

In this talk we discuss the problem of evaluating some exotic versions of cubic moments of Dirichlet L-functions of large modulus: namely

$$\sum_{\chi(q)} L(\chi^a,1/2)L(\chi^b,1/2)L(\chi^c,1/2)$$

where $q$ is a growing prime and $a,b,c$ are integers that are not necessarily equal (the pure case $a=b=c=1$ is the usual cubic moment for Dirichlet L-functions and its evaluation is closely related to the famous work of Friedlander-Iwaniec on the ternary divisor function in large arithmetic progressions).

We will discuss some partial results on this problem (which is not solved in full generality at this moment) using non trivial bounds for solutions to polynomial congruences as well as for averages of hyper-Kloosterman sums in short intervals. This is joint work with E. Fouvry, E. Kowalski and W. Sawin.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].