p -adic interpolation of convolutions of Hilbert modular forms

Volker Dünger

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 2, page 365-428
  • ISSN: 0373-0956

Abstract

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In this paper we construct p -adic measures related to the values of convolutions of Hilbert modular forms of integral and half-integral weight at the negative critical points under the assumption that the underlying totally real number field F has class number h F = 1 . This extends the result of Panchishkin [Lecture Notes in Math., 1471, Springer Verlag, 1991 ] who treated the case that both modular forms are of integral weight. In order to define the measures, we need to introduce the twist operator and a certain inverter j on the space of Hilbert modular forms of half-integral weight. The proof then makes use of the Rankin-Selberg integral representation of the convolution and of explicit formulas for the Fourier coefficients of certain Eisenstein series of half-integral weight derived by Shimura [Duke Math. J., 52 (1985), 281-314].

How to cite

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Dünger, Volker. "$p$-adic interpolation of convolutions of Hilbert modular forms." Annales de l'institut Fourier 47.2 (1997): 365-428. <http://eudml.org/doc/75233>.

@article{Dünger1997,
abstract = {In this paper we construct $p$-adic measures related to the values of convolutions of Hilbert modular forms of integral and half-integral weight at the negative critical points under the assumption that the underlying totally real number field $F$ has class number $h_F=1$. This extends the result of Panchishkin [Lecture Notes in Math., 1471, Springer Verlag, 1991 ] who treated the case that both modular forms are of integral weight. In order to define the measures, we need to introduce the twist operator and a certain inverter $j$ on the space of Hilbert modular forms of half-integral weight. The proof then makes use of the Rankin-Selberg integral representation of the convolution and of explicit formulas for the Fourier coefficients of certain Eisenstein series of half-integral weight derived by Shimura [Duke Math. J., 52 (1985), 281-314].},
author = {Dünger, Volker},
journal = {Annales de l'institut Fourier},
keywords = {-adic interpolation; Hilbert modular forms; half-integral weight; convolution},
language = {eng},
number = {2},
pages = {365-428},
publisher = {Association des Annales de l'Institut Fourier},
title = {$p$-adic interpolation of convolutions of Hilbert modular forms},
url = {http://eudml.org/doc/75233},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Dünger, Volker
TI - $p$-adic interpolation of convolutions of Hilbert modular forms
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 2
SP - 365
EP - 428
AB - In this paper we construct $p$-adic measures related to the values of convolutions of Hilbert modular forms of integral and half-integral weight at the negative critical points under the assumption that the underlying totally real number field $F$ has class number $h_F=1$. This extends the result of Panchishkin [Lecture Notes in Math., 1471, Springer Verlag, 1991 ] who treated the case that both modular forms are of integral weight. In order to define the measures, we need to introduce the twist operator and a certain inverter $j$ on the space of Hilbert modular forms of half-integral weight. The proof then makes use of the Rankin-Selberg integral representation of the convolution and of explicit formulas for the Fourier coefficients of certain Eisenstein series of half-integral weight derived by Shimura [Duke Math. J., 52 (1985), 281-314].
LA - eng
KW - -adic interpolation; Hilbert modular forms; half-integral weight; convolution
UR - http://eudml.org/doc/75233
ER -

References

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