Jolanta Marzec

University of Silesia


Some evidence towards Resnikoff-Saldana conjecture


Heilbronn Number Theory Seminar


1st December 2021, 4:00 pm – 5:00 pm
Fry Building, online


The Resnikoff-Saldana conjecture proposes a bound for Fourier coefficients of Siegel modular forms of any degree, generalizing the classical Ramanujan-Petersson conjecture. In the talk we consider the case of degree 2. We show that the conjecture holds for many (to be specified) Fourier coefficients of Siegel modular forms which are not generalized Saito-Kurokawa lifts, as long as it holds for the ones that are fundamental. To do this we employ relations between Fourier coefficients, local Bessel periods and Satake parameters, ultimately translating a result of Weissauer on the generalized Ramanujan-Petersson conjecture to a bound for Fourier coefficients.






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