Number Theory Seminar

Deligne's conjecture predicts that the special values of L-functions of automorphic forms at critical points are algebraic up to certain prescribed transcendental factors. There is a lot of literature on progress towards this conjecture for various classes of automorphic forms. In this talk, we will present new results for the degree 5 standard L-functions of genus 2 holomorphic Siegel modular forms. The main step is to obtain an integral representation of the L-function, which we are able to do for general genus n. Using results of Ramakrishnan and Shahidi, the genus 2 special value result allows us to obtain the algebraicity of the symmetric fourth L-function of an elliptic cusp form twisted by characters. This is joint work with Abhishek Saha and Ralf Schmidt.