Washington State
University
Combinatorics, Linear Algebra and Number Theory Seminar
Department of Mathematics and Statistics
Zoom
March 7, Monday, 4:10 - 5:00 PM
Jennifer Johnson-Leung
Department of Mathematics and Statistics
University of Idaho
Combinatorics, Linear Algebra and Number Theory Seminar
Department of Mathematics and Statistics
Zoom
March 7, Monday, 4:10 - 5:00 PM
Jennifer Johnson-Leung
Department of Mathematics and Statistics
University of Idaho
Title: Klingen Vectors and Siegel Paramodular
Forms
Abstract: The Hecke eigenvalues of classical modular forms are realized in the Fourier expansions of eigenforms. For Siegel modular forms, the situation is more complicated. In this talk, I will present joint work with Brooks Roberts and Ralf Schmidt in which we develop a theory of stable Klingen vectors inside of paramodular representations with sufficient ramification. Using this theory, we give a method for rapid calculations of Hecke eigenvalues of ramified primes from the Fourier coefficients of Siegel modular forms with paramodular level divisible by a square. In addition, we obtain a generalization of Andrianov's rationality result for a certain Dirichlet series of Fourier coefficients.
Abstract: The Hecke eigenvalues of classical modular forms are realized in the Fourier expansions of eigenforms. For Siegel modular forms, the situation is more complicated. In this talk, I will present joint work with Brooks Roberts and Ralf Schmidt in which we develop a theory of stable Klingen vectors inside of paramodular representations with sufficient ramification. Using this theory, we give a method for rapid calculations of Hecke eigenvalues of ramified primes from the Fourier coefficients of Siegel modular forms with paramodular level divisible by a square. In addition, we obtain a generalization of Andrianov's rationality result for a certain Dirichlet series of Fourier coefficients.