On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields

Haruzo Hida

Annales de l'institut Fourier (1991)

  • Volume: 41, Issue: 2, page 311-391
  • ISSN: 0373-0956

Abstract

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Let D ( s , f , g ) be the Rankin product L -function for two Hilbert cusp forms f and g . This L -function is in fact the standard L -function of an automorphic representation of the algebraic group G L ( 2 ) × G L ( 2 ) defined over a totally real field. Under the ordinarity assumption at a given prime p for f and g , we shall construct a p -adic analytic function of several variables which interpolates the algebraic part of D ( m , f , g ) for critical integers m , regarding all the ingredients m , f and g as variables.

How to cite

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Hida, Haruzo. "On $p$-adic $L$-functions of $GL(2)\times GL(2)$ over totally real fields." Annales de l'institut Fourier 41.2 (1991): 311-391. <http://eudml.org/doc/74922>.

@article{Hida1991,
abstract = {Let $D(s,f,g)$ be the Rankin product $L$-function for two Hilbert cusp forms $f$ and $g$. This $L$-function is in fact the standard $L$-function of an automorphic representation of the algebraic group $GL(2)\times GL(2)$ defined over a totally real field. Under the ordinarity assumption at a given prime $p$ for $f$ and $g$, we shall construct a $p$-adic analytic function of several variables which interpolates the algebraic part of $D(m,f,g)$ for critical integers $m$, regarding all the ingredients $m$, $f$ and $g$ as variables.},
author = {Hida, Haruzo},
journal = {Annales de l'institut Fourier},
keywords = {interpolation; Rankin product -function; Hilbert cusp forms; automorphic representation; -adic analytic function},
language = {eng},
number = {2},
pages = {311-391},
publisher = {Association des Annales de l'Institut Fourier},
title = {On $p$-adic $L$-functions of $GL(2)\times GL(2)$ over totally real fields},
url = {http://eudml.org/doc/74922},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Hida, Haruzo
TI - On $p$-adic $L$-functions of $GL(2)\times GL(2)$ over totally real fields
JO - Annales de l'institut Fourier
PY - 1991
PB - Association des Annales de l'Institut Fourier
VL - 41
IS - 2
SP - 311
EP - 391
AB - Let $D(s,f,g)$ be the Rankin product $L$-function for two Hilbert cusp forms $f$ and $g$. This $L$-function is in fact the standard $L$-function of an automorphic representation of the algebraic group $GL(2)\times GL(2)$ defined over a totally real field. Under the ordinarity assumption at a given prime $p$ for $f$ and $g$, we shall construct a $p$-adic analytic function of several variables which interpolates the algebraic part of $D(m,f,g)$ for critical integers $m$, regarding all the ingredients $m$, $f$ and $g$ as variables.
LA - eng
KW - interpolation; Rankin product -function; Hilbert cusp forms; automorphic representation; -adic analytic function
UR - http://eudml.org/doc/74922
ER -

References

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Citations in EuDML Documents

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  1. Haruzo Hida, p -adic ordinary Hecke algebras for GL ( 2 )
  2. Andrzej Dabrowski, p -adic L -functions of Hilbert modular forms
  3. H. Hida, J. Tilouine, Anti-cyclotomic Katz p -adic L -functions and congruence modules
  4. Haruzo Hida, On the search of genuine p -adic modular L -functions for G L ( n ) . With a correction to: On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields
  5. Alexei A. Panchishkin, Motives over totally real fields and p -adic L -functions

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