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Article Dans Une Revue Contemporary mathematics Année : 2014

A p-adic integral for the reciprocal of L-functions

Stephen Gelbart
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Stephen D. Miller
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Alexei Pantchichkine
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Résumé

This interesting article suggests a far-reaching programme for constructing p-adic interpolation series for special values of automorphic L-functions appearing as Fourier coefficients of Eisenstein series on arbitrary reductive groups. Namely, it suggests a programme for developing p-adic analogues of the Langlands-Shahidi method (rather than the more conventional approach using integral presentations) to make such constructions. The body of the article deals with the classical setting of Eisenstein series on SL(2), and gives in §3 a construction of a p-adic measure via the (nonvanishing) Fourier coefficients which coincides with Mazur's measure (as shown via purely algebraic arguments in §4). However, it is suggested that by using spectral theory and the modern theory of Eisenstein series, the general setting could eventually be treated this way.
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Dates et versions

hal-01990543 , version 1 (23-01-2019)

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  • HAL Id : hal-01990543 , version 1

Citer

Stephen Gelbart, Stephen D. Miller, Alexei Pantchichkine. A p-adic integral for the reciprocal of L-functions. Contemporary mathematics, 2014, Automorphic forms and related geometry: assessing the legacy of I. I. Piatetski-Shapiro, 614, pp.53-68. ⟨hal-01990543⟩

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