Titlebook: Siegel Modular Forms; A Classical and Repr Ameya Pitale Book 2019 Springer Nature Switzerland AG 2019 Siegel modular forms.Symplectic group

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Applications of Properties of ,-Functions,In this chapter, we present two applications of properties of .-functions of Siegel modular forms. The first one is to determine whether a given modular form is a cusp form based on the size of its Fourier coefficients.

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Local Representation Theory of ,In this chapter, we will discuss the representation theory of .. The genus 2 case provides a very good introduction to the study of local representations of the symplectic groups. The genus 2 case also has the advantage of detailed tables of data compiled by Roberts and Schmidt.

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Bessel Models and Applications,Holomorphic Siegel modular forms . correspond to cuspidal automorphic representations . of . that are not globally generic, i.e., they do not have a global Whittaker model.

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Analytic and Arithmetic Properties of , ,-Functions,In this chapter, we will start from the integral representation for . obtained in the previous chapter. We will use this integral representation to obtain analytic and arithmetic properties of the .-functions. We will also present several applications.

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978-3-030-15674-9Springer Nature Switzerland AG 2019

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https://doi.org/10.1007/978-3-030-15675-6Siegel modular forms; Symplectic group; Automorphic representations; L-functions; Fourier coefficients; D

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Examples,ito–Kurokawa lifts. These are concrete examples of cuspidal Siegel modular forms constructed from elliptic cusp forms. Finally, we consider Siegel modular forms with level . in the genus . case, corresponding to the standard congruence subgroups.