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Asymptotic behaviour of the Euler-Kronecker constant. (English) Zbl 1185.11070
Ginzburg, Victor (ed.), Algebraic geometry and number theory. In Honor of Vladimir Drinfeld’s 50th birthday. Basel: Birkhäuser (ISBN 978-0-8176-4471-0/hbk). Progress in Mathematics 253, 453-458 (2006).
This is an appendix to Y. Ihara’s paper [Prog. Math. 253, 407–451 (2006; Zbl 1185.11069)]. Let \(K\) be a number field with discriminant \(d_K\) and Euler-Kronecker constant \(\gamma_K\). Under the generalized Riemann hypothesis the author proves that \[ \liminf_K\frac{\gamma_K}{\log \sqrt{|d_K|}} \geq -0.26049... . \] He produces examples of class-field towers , showing that \[ \liminf_K\frac{\gamma_K}{\log \sqrt{|d_K|}} \leq -0.17849... . \]
For the entire collection see [Zbl 1113.00007].

MSC:
11R42 Zeta functions and \(L\)-functions of number fields
11R47 Other analytic theory
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