Number Theory Seminar

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.