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
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
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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
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