Characteristic twists of a Dirichlet series for Siegel cusp forms (original) (raw)

Characteristic twists of a Dirichlet series for Siegel cusp forms are explored in this work, focusing on the relationship between these twists and various mathematical constructs such as Petersson inner products, Hecke eigenforms, and the Andrianov zeta function. The study derives significant relationships and provides multiple theorems, including conditions under which certain inner products vanish or yield results linked to primitive Dirichlet characters. Additionally, the implications of these findings on the behavior of special functions and modular forms are discussed.