Ramon M. Nunes (Universidade Federal do Ceará): Integral representations of $L$-functions and spectral identities

Abstract: In recent years a lot of attention has been given to the study of spectral identities between moments of automorphic $L$-functions. Besides their intrinsic beauty, these formulas are also very powerful as one is able to deduce interesting information about moments without performing a delicate study of the geometric side of a trace formula. In this talk I will show some instances of spectral identities in the literature and show a recent result obtained jointly with Subhajit Jana on a higher rank spectral identity which relates mixed moments of certain Rankin-Selberg $L$-functions on $\mathrm{GL}_n$.

The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.