On the rationality of period integrals and special value formulas in the compact case
Rendiconti del Seminario Matematico della Università di Padova, Tome 143 (2020), pp. 35-80.
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We study rationality properties of period integrals that appear in the Gan–Gross–Prasad conjectures in the compact case using Gross’ theory of algebraic modular forms. In situations where the refined Gan–Gross–Prasad are known, our rationality result for period can be interpreted as a special value formula for automorphic -functions which proves automorphic versions of Deligne’s conjecture on rationality of periods. Moreover, this special value formula is well suited to -adic interpolation, as illustrated in [10].
Publié le :
DOI : 10.4171/RSMUP/39
DOI : 10.4171/RSMUP/39
Classification :
11, 00
Mots clés : Special values of $L$-functions, Gan–Gross–Prasad conjecture, algebraic modular forms
Mots clés : Special values of $L$-functions, Gan–Gross–Prasad conjecture, algebraic modular forms
Affiliations des auteurs :
Greenberg, Matthew 1 ;
Seveso, Marco Adamo 2
@article{RSMUP_2020__143__35_0,
author = {Greenberg, Matthew and Seveso, Marco Adamo},
title = {On the rationality of period integrals and special value formulas in the compact case},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {35--80},
publisher = {European Mathematical Society Publishing House},
address = {Zuerich, Switzerland},
volume = {143},
year = {2020},
doi = {10.4171/RSMUP/39},
mrnumber = {4103739},
zbl = {1458.11079},
url = {http://archive.numdam.org/articles/10.4171/RSMUP/39/}
}
TY - JOUR AU - Greenberg, Matthew AU - Seveso, Marco Adamo TI - On the rationality of period integrals and special value formulas in the compact case JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2020 SP - 35 EP - 80 VL - 143 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://archive.numdam.org/articles/10.4171/RSMUP/39/ DO - 10.4171/RSMUP/39 ID - RSMUP_2020__143__35_0 ER -
%0 Journal Article %A Greenberg, Matthew %A Seveso, Marco Adamo %T On the rationality of period integrals and special value formulas in the compact case %J Rendiconti del Seminario Matematico della Università di Padova %D 2020 %P 35-80 %V 143 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://archive.numdam.org/articles/10.4171/RSMUP/39/ %R 10.4171/RSMUP/39 %F RSMUP_2020__143__35_0
Greenberg, Matthew; Seveso, Marco Adamo. On the rationality of period integrals and special value formulas in the compact case. Rendiconti del Seminario Matematico della Università di Padova, Tome 143 (2020), pp. 35-80. doi : 10.4171/RSMUP/39. http://archive.numdam.org/articles/10.4171/RSMUP/39/
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