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Washington State University
Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics
  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
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.