Non-Archimedean convolutions of Hilbert modular forms

  • Alexey A. Panchishkin
Part of the Lecture Notes in Mathematics book series (LNM, volume 1471)


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


Fourier Coefficient Galois Group Fourier Expansion Eisenstein Series Cusp Form 
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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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