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- W2182361844 abstract "A classical result of Chowla [Improvement of a theorem of Linnik and Walfisz, Proc. London Math. Soc. (2) 50 (1949) 423–429 and The Collected Papers of Sarvadaman Chowla, Vol. 2 (Centre de Recherches Mathematiques, 1999), pp. 696–702] states that for infinitely many fundamental discriminants D we have [Formula: see text] where χ D is the quadratic Dirichlet character of conductor D. In this paper, we prove an analogous result for the logarithmic derivative [Formula: see text], and investigate the growth of the logarithmic derivatives of real Dirichlet L-functions. We show that there are infinitely many fundamental discriminants D (both positive and negative) such that [Formula: see text] and infinitely many fundamental discriminants 0 < D such that [Formula: see text] In particular, we show that the Euler–Kronecker constant γ K of a quadratic field K satisfies γ K = Ω( log log |d K |). We get sharper results assuming the GRH. Moreover, we evaluate the moments of [Formula: see text]." @default.
- W2182361844 created "2016-06-24" @default.
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- W2182361844 date "2013-04-07" @default.
- W2182361844 modified "2023-10-02" @default.
- W2182361844 title "OMEGA THEOREMS FOR $frac{L'}{L}(1, chi_D)$" @default.
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- W2182361844 doi "https://doi.org/10.1142/s1793042112501485" @default.
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