On the rationality of period integrals and special value formulas in the compact case
Greenberg, Matthew1 ; Seveso, Marco Adamo2
1 University of Calgary, Canada
2 Università degli Studi di Milano, Italy
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 L-functions which proves automorphic versions of Deligne’s conjecture on rationality of periods. Moreover, this special value formula is well suited to p-adic interpolation, as illustrated in [10].

Publié le :
DOI : 10.4171/RSMUP/39
Classification : 11, 00
Mots-clés : Special values of $L$-functions, Gan–Gross–Prasad conjecture, algebraic modular forms
Greenberg, Matthew 1 ; Seveso, Marco Adamo 2

1 University of Calgary, Canada
2 Università degli Studi di Milano, Italy 
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     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},
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     year = {2020},
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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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