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

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.

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DOI : https://doi.org/10.5802/jtnb.785
Mots clés : cuspidal automorphic L-functions, regularized products (determinants), explicit formulas, grand Riemann hypothesis.
@article{JTNB_2011__23_3_751_0,
     author = {Masato Wakayama and Yoshinori Yamasaki},
     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://jtnb.centre-mersenne.org/articles/10.5802/jtnb.785/}
}
Masato Wakayama; Yoshinori Yamasaki. 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://jtnb.centre-mersenne.org/articles/10.5802/jtnb.785/

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