We construct p-adic triple product L-functions that interpolate (square roots of) central critical L-values in the balanced region. Thus, our construction complements that of Harris and Tilouine. There are four central critical regions for the triple product L-functions and two opposite settings, according to the sign of the functional equation. In the first case, three of these regions are of interpolation, having positive sign; they are called the unbalanced regions and one gets three p-adic L-functions, one for each region of interpolation (this is the Harris-Tilouine setting). In the other setting there is only one region of interpolation, called the balanced region: we produce the corresponding p-adic L-function. Our triple product p-adic L-function arises as p-adic period integrals interpolating normalizations of the local archimedean period integrals. The latter encode information about classical representation theoretic branching laws. The main step in our construction of p-adic period integrals is showing that these branching laws vary in a p-adic analytic fashion. This relies crucially on the Ash-Stevens theory of highest weight representations over affinoid algebras.
Triple product p-adic L-functions for balanced weights / M. Greenberg, M.A. Seveso. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 376:1-2(2020), pp. 103-176.
|Titolo:||Triple product p-adic L-functions for balanced weights|
SEVESO, MARCO ADAMO (Corresponding)
|Settore Scientifico Disciplinare:||Settore MAT/02 - Algebra|
|Data di pubblicazione:||2020|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s00208-019-01865-w|
|Appare nelle tipologie:||01 - Articolo su periodico|
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