Dedekind Sums, Mean Square Value of L-Functions at s = 1 and Upper Bounds on Relative Class Numbers

• Autorzy: Louboutin S.

Identyfikatory

DOI

10.4064/ba8092-12-2016

• Języki publikacji: EN

Abstrakty

EN

Explicit formulas for the quadratic mean value at s = 1 of the Dirichlet L-functions associated with the set X_f¯ of the ϕ(f)/2 odd Dirichlet characters mod f are known. They have been used to obtain explicit upper bounds for relative class numbers of cyclotomic number fields. Here we present a generalization of these results: we show that explicit formulas for quadratic mean values at s = 1 of Dirichlet L-functions associated with subsets of X_f¯ can be obtained. As an application we use them to obtain explicit upper bounds for relative class numbers of imaginary subfields of cyclotomic number fields.

Słowa kluczowe

EN

Dirichlet character; L-function; mean square value; relative class number; Dedekind sums; cyclotomic field

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2016
• Tom: Vol. 64, no. 2/3
• Strony: 165--174
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Louboutin S.

• Aix Marseille Université CNRS, Centrale Marseille, I2M, Marseille, France

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.