St'ephane Louboutin

collaborators

3 papers

math.NT2025

Ideal class groups of some quadratic number fields and factorization of values of some quadratic polynomials

StÃ©phane Louboutin

We fill the gaps in A. Gica's determination of all the odd positive integers $d$ for which the number of distinct prime divisors of $f_{d} (x) = d + x^{2}$ is less than or equal to $2$ for…

math.NT2024

Dedekind sums and mean square value of $L (1, I ¨ )$ over subgroups

StÃ©phane Louboutin

An explicit formula for the quadratic mean value at $s = 1$ of the Dirichlet $L$ -functions associated with the odd Dirichlet characters modulo $f > 2$ is known. Here we present a situa…

math.NT2024

Explicit formulae for the mean value of products of values of Dirichlet $L$ -functions at positive integers

Let $m \geq 1$ be a rational integer. We give an explicit formula for the mean value $\frac{2}{I ¨ ( f )} I ¨ (- 1) = (- 1)^{m} \sum ∣ L (m, I ¨ ) ∣^{2},$ where $I ¨ $ ranges over the $I ¨ (f) /2$ …

Ideal class groups of some quadratic number fields and factorization of values of some quadratic polynomials

Dedekind sums and mean square value of L(1,I¨) over subgroups

Explicit formulae for the mean value of products of values of Dirichlet L-functions at positive integers

Dedekind sums and mean square value of $L (1, I ¨ )$ over subgroups

Explicit formulae for the mean value of products of values of Dirichlet $L$ -functions at positive integers