Number Theory Seminar

Speaker: Johannes Linn (Bonn)

Title: Bounds for Kloosterman Sums for GL_n

Abstract: Classical Kloosterman sums defined by S(m,n;c)=∑_{x∈ (ℤ/cℤ)^*} e((mx+nx)/c) for m,n∈ℤ and c∈ℤ⁺ have become ubiquitous in  Number Theory appearing for example in Fourier coefficients of classical Poincaré series and therefore in the geometric side of relative trace formulae of Petersson-Kuznetsov type. Working with relative trace formulae over GL_n requires understanding of more general Kloosterman sums. In this talk, I will present a method to parametrize and bound the generalized Kloosterman sums for GL_n, obtaining a power saving compared to the trivial bound and gaining insight into their structure.