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Non-Archimedean convolutions of Hilbert modular forms

  • Alexey A. Panchishkin
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alexey A. Panchishkin
    • 1
  1. 1.Department of MathematicsMoscow State UniversityMoscowUSSR

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