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Non-Archimedean convolutions of Hilbert modular forms

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1471)

Abstract

Now let p be a prime number and S a finite set of primes containing p. In this chapter we consider convolutions of Hilbert modular forms and construct their S-adic analogues; they correspond to certain automorphic forms on the group G = GL2 × GL2 over a totally real field F and have the form

$$L(s,f,g) = \mathop \Sigma \limits_n C(n,f)C(n,g)N(n)^{ - s} ,$$
(0.1)

where f, g are Hilbert automorphic forms of “holomorphic type” over F, and C(n, f), C(n, g) are their normalized Fourier coefficients (indexed by integral ideals n of the maximal order O F F).

Keywords

  • Fourier Coefficient
  • Galois Group
  • Fourier Expansion
  • Eisenstein Series
  • Cusp Form

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1991 Springer-Verlag Berlin Heidelberg

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Panchishkin, A.A. (1991). Non-Archimedean convolutions of Hilbert modular forms. In: Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms. Lecture Notes in Mathematics, vol 1471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21541-8_6

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  • DOI: https://doi.org/10.1007/978-3-662-21541-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54137-0

  • Online ISBN: 978-3-662-21541-8

  • eBook Packages: Springer Book Archive