Higher regularizations of zeros of cuspidal automorphic $L$-functions of ${\rm GL}_d$

Wakayama, Masato; Yamasaki, Yoshinori

doi:10.5802/jtnb.785

Higher regularizations of zeros of cuspidal automorphic

L

-functions of

{GL}_{d}

Wakayama, Masato ¹ ; Yamasaki, Yoshinori ²

¹ Faculty of Mathematics Kyushu University Motooka, Nishiku, Fukuoka 819-0395, JAPAN
² Graduate School of Science and Engineering Ehime University Bunkyo-cho, Matsuyama 790-8577, JAPAN

Journal de théorie des nombres de Bordeaux, Tome 23 (2011) no. 3, pp. 751-767.

Résumé
Abstract

Nous établissons un analogue de la “plus haute profondeur” des déterminants régularisés due à Milnor pour les zéros des fonctions $L$ automorphes cuspidales de ${GL}_{d}$ sur un corps de nombres général. C’est une généralisation du résultat de Deninger au sujet du déterminant régularisé pour les zéros de la fonction zêta de Riemann.

We establish “higher depth” analogues of regularized determinants due to Milnor for zeros of cuspidal automorphic $L$ -functions of ${GL}_{d}$ over a general number field. This is a generalization of the result of Deninger about the regularized determinant for zeros of the Riemann zeta function.

MR Zbl

DOI : 10.5802/jtnb.785

Mots-clés : cuspidal automorphic

L

-functions, regularized products (determinants), explicit formulas, grand Riemann hypothesis.

Affiliations des auteurs :

Wakayama, Masato ¹ ; Yamasaki, Yoshinori ²

¹ Faculty of Mathematics Kyushu University Motooka, Nishiku, Fukuoka 819-0395, JAPAN
² Graduate School of Science and Engineering Ehime University Bunkyo-cho, Matsuyama 790-8577, JAPAN

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     title = {Higher regularizations of zeros of cuspidal automorphic $L$-functions of ${\rm GL}_d$},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {751--767},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {23},
     number = {3},
     year = {2011},
     doi = {10.5802/jtnb.785},
     zbl = {1270.11055},
     mrnumber = {2861083},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/jtnb.785/}
}

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Wakayama, Masato; Yamasaki, Yoshinori. Higher regularizations of zeros of cuspidal automorphic $L$-functions of ${\rm GL}_d$. Journal de théorie des nombres de Bordeaux, Tome 23 (2011) no. 3, pp. 751-767. doi : 10.5802/jtnb.785. https://www.numdam.org/articles/10.5802/jtnb.785/

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