Twisted quadratic moments for Dirichlet L-functions at s = 2

Stéphane Louboutin (1)

1 I2M - Institut de Mathématiques de Marseille

Let c, n be given positive integers. Let q > 2 be coprime with c. Let X q be the multiplicative group of order φ(q) of the Dirichlet characters modulo q. Set M (q, c, n) := 2 φ(q) χ∈Xq χ(−1)=(−1) n χ(c)|L(n, χ)| 2. The goal of this paper is to explain how one can compute explicit formulas for M (q, c, n) for a given small integers n and c. As an example, we give explicit formulas for M (q, c, 2) for c ∈ {1, 2, 3, 4, 6} and for M (p, 5, 2) for p a prime integer. As a consequence, we show that a previously published formula for M (p, 3, 2) is false. 0 2010 Mathematics Subject Classification. Primary. 11M06.

Mots clés: Dirichlet L-functions; mean values; quadratic moments

Domaines: Théorie des nombres [math.NT]

Stéphane Louboutin. Twisted quadratic moments for Dirichlet L-functions at s = 2. Publ. Math. Debrecen, In press. ⟨hal-02111813⟩