Extremal values of Dirichlet L-functions in the half-plane of absolute convergence
Journal de Théorie des Nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 221-232.

On démontre que, pour tout θ réel, il existe une infinité de s=σ+it avec σ1+ et t+ tel que

{exp(iθ)logL(s,χ)}loglogloglogtloglogloglogt+O(1).

La démonstration est basée sur une version effective du théorème de Kronecker sur les approximations diophantiennes.

We prove that for any real θ there are infinitely many values of s=σ+it with σ1+ and t+ such that

{exp(iθ)logL(s,χ)}loglogloglogtloglogloglogt+O(1).

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

@article{JTNB_2004__16_1_221_0,
     author = {J\"orn Steuding},
     title = {Extremal values of Dirichlet $L$-functions in the half-plane of absolute convergence},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {221--232},
     publisher = {Universit\'e Bordeaux 1},
     volume = {16},
     number = {1},
     year = {2004},
     doi = {10.5802/jtnb.444},
     zbl = {1069.11036},
     mrnumber = {2145583},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_2004__16_1_221_0/}
}
Jörn Steuding. Extremal values of Dirichlet $L$-functions in the half-plane of absolute convergence. Journal de Théorie des Nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 221-232. doi : 10.5802/jtnb.444. https://jtnb.centre-mersenne.org/item/JTNB_2004__16_1_221_0/

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