Joint IAS/Princeton University Number Theory Seminar

Non-spherical Poincaré series, cusp forms and L-functions for $GL(3)$

The analytic theory of Poincaré series and Maass cusp forms and their L-functions for $SL(3,Z)$ has, so far, been limited to the spherical Maass forms, i.e. elements of a spectral basis for $L^2(SL(3,Z)\PSL(3,R)/SO(3,R))$. I will describe the Maass cusp forms of $L^2(SL(3,Z)\PSL(3,R))$ which are minimal with respect to the action of the Lie algebra and give a (relatively) simple method for constructing Kuznetsov-type trace formulas by considering Fourier coefficients of certain Poincaré series. In recent work with Valentin Blomer, we have extended our proof of spectral-aspect subconvexity for L-functions of $SL(3,Z)$ Maass forms to the non-spherical case, and I will discuss the structure of that proof, as well.

Date & Time

April 10, 2018 | 4:45pm – 5:45pm

Location

Simonyi Hall 101

Speakers

Jack Buttcane

Affiliation

University of Buffalo

Event Series

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