Steuding: Extremal values of Dirichlet $L$-functions in the half-plane of absolute convergence

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Jörn Steuding
Extremal values of Dirichlet $L$-functions in the half-plane of absolute convergence
Journal de théorie des nombres de Bordeaux, 16 no. 1 (2004), p. 221-232, doi: 10.5802/jtnb.444
Article PDF | Reviews MR 2145583 | Zbl 1069.11036

Résumé - Abstract

We prove that for any real $\theta $ there are infinitely many values of $s=\sigma +it$ with $\sigma \rightarrow 1+$ and $t\rightarrow +\infty $ such that

$$ \Re \lbrace \exp (i\theta )\log L(s,\chi )\rbrace \ge \log {\log \log \log t \over \log \log \log \log t}+O(1).$$

The proof relies on an effective version of Kronecker’s approximation theorem.

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