# 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/π^{2} √(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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