Higher regularizations of zeros of cuspidal automorphic L-functions of GL d
Journal de théorie des nombres de Bordeaux, Volume 23 (2011) no. 3, pp. 751-767.

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.

DOI: 10.5802/jtnb.785
Keywords: cuspidal automorphic L-functions, regularized products (determinants), explicit formulas, grand Riemann hypothesis.
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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Wakayama, Masato; Yamasaki, Yoshinori. 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. http://archive.numdam.org/articles/10.5802/jtnb.785/

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