Explicit zero-free regions for Dedekind Zeta functions
Kadiri, Habiba
arXiv, 1106.1868 / Harvested from arXiv
Text on arXiv
Let K be a number field, n_K its degree, and d_K the absolute value of its discriminant. We prove that, if d_K is sufficiently large, then the Dedekind zeta function associated to K has no zeros in the region: Re(s) > 1 - 1/(12.55 log d_K + 9.69 n_K log|Im s| + 3.03 n_K + 58.63) and |Im s| > 1. Moreover, it has at most one zero in the region: Re (s) > 1- 1/(12.74 log d_K) and |Im s| < 1. This zero if it exists is simple and is real. This argument also improves a result of Stark by a factor of 2: there is at most one zero in the region Re (s) > 1 - 1/(2 log d_K) and |Im s| < 1/(2 log d_K).
Publié le : 2011-06-09
Classification:  Mathematics - Number Theory,  Primary 11M41, Secondary 11R42, 11M26 
@article{1106.1868,
     author = {Kadiri, Habiba},
     title = {Explicit zero-free regions for Dedekind Zeta functions},
     journal = {arXiv},
     volume = {2011},
     number = {0},
     year = {2011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1106.1868}
}

Kadiri, Habiba. Explicit zero-free regions for Dedekind Zeta functions. arXiv, Tome 2011 (2011) no. 0, . http://gdmltest.u-ga.fr/item/1106.1868/