# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

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

### Tom 64 / 2016

Bulletin Polish Acad. Sci. Math. 64 (2016), 165-174 MSC: Primary 11R42; Secondary 11M20, 11R20, 11R29. DOI: 10.4064/ba8092-12-2016 Opublikowany online: 14 December 2016

#### Streszczenie

Explicit formulas for the quadratic mean value at $s=1$ of the Dirichlet $L$-functions associated with the set $X_f^-$ of the $\phi (f)/2$ 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.

#### Autorzy

• Stéphane R. LouboutinAix Marseille Université CNRS, Centrale Marseille, I2M
Marseille, France
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek