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Washington State
University

Combinatorics, Linear Algebra and Number Theory Seminar

Department of Mathematics and Statistics

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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.