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

Masato Wakayama; Yoshinori Yamasaki

doi:10.5802/jtnb.785

Higher regularizations of zeros of cuspidal automorphic

L

-functions of

{GL}_{d}

Masato Wakayama ¹; Yoshinori Yamasaki 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, Volume 23 (2011) no. 3, pp. 751-767.

Abstract
Résumé

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.

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.

MR Zbl

DOI: 10.5802/jtnb.785

Keywords: cuspidal automorphic $L$-functions, regularized products (determinants), explicit formulas, grand Riemann hypothesis.

Author's affiliations:

Masato Wakayama ¹; Yoshinori Yamasaki 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},
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     zbl = {1270.11055},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.785/}
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Masato Wakayama; Yoshinori Yamasaki. Higher regularizations of zeros of cuspidal automorphic $L$-functions of ${\rm GL}_d$. Journal de théorie des nombres de Bordeaux, Volume 23 (2011) no. 3, pp. 751-767. doi : 10.5802/jtnb.785. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.785/

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