Moscow Mathematical Journal

Volume 15, Issue 3, July–September 2015 pp. 497–509.

Distribution of values of L′/L(σ,χ_D)

Authors: Mariam Mourtada and V. Kumar Murty
Author institution:Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4

Summary:

We study the distribution of values of L′/L(σ, χ_D), where σ is real >1/2, D a fundamental discriminant, and χ_D the real character attached to D. In particular, assuming the GRH, we prove that for each σ>1/2 there is a density function 𝒬_σ with the property that for real numbers α≤β, we have

#{D fundamental discriminants such that |D|≤Y, and α ≤ L′/L(σ, χ_D) ≤ β } ∼ (6/π² √(2π)) Y ∫_α^β 𝒬_σ (x)dx

Our work is based on and strongly motivated by the earlier work of Ihara and Matsumoto.

2010 Math. Subj. Class. 11M06, 11M26.

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