Xuanxuan Xiao

Xuanxuan Xiao, IECL, Université de Lorraine

Higher moments of automorphic L-functions in short intervals

In analytic number theory, estimate for the moments of Riemann zeta function is an important problem. Under RH, the upper and lower bounds for higher moments are proved thanks to the work of Heath-Brown, Soundararajan and Harper.

We study the analogue of the problem, the moments of the automorphic L-functions in short intervals, and prove, for all r > 0 and T^ε < H < T,

H(log T)^r² << ∫_{_T}^{^T+H} |L(½ + iτ, f)|^2rdτ << H(log T)^r², under GRH for L(s, f).