## 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

### Keywords:

algebraic number field; Euler-Kronecker constant

Zbl 1185.11069
Full Text: