One more proof of Siegel's theorem
Ramachandra, K
HAL, hal-01103859 / Harvested from HAL
Text on HAL
This paper gives a new elementary proof of the version of Siegel's theorem on $L(1,\chi)=\sum_{n=1}^{\infty}\chi(n)n^{-1}$ for a real character $\chi(\!\!\!\!\mod k)$. The main result of this paper is the theorem: If $3\leq k_1\leq k_2$ are integers, $\chi_1(\!\!\!\!\mod k_1)$ and $\chi_2(\!\!\!\!\mod k_2)$ are two real non-principal characters such that there exists an integer $n>0$ for which $\chi_1(n)\cdot\chi_2(n)=-1$ and, moreover, if $L(1,\chi_1)\leq10^{-40}(\log k_1)^{-1}$, then $L(1,\chi_2)>10^{-4} (\log k_2){-1}\cdot(\log k_1)^{-2}k_2^{-40000L(1,\chi_1)}$. From this the result of T. Tatuzawa on Siegel's theorem follows.
Publié le : 1980-07-04
Classification:  Siegel's theorem,  real characters,  Polya-Vinogradov inequality,  [MATH]Mathematics [math] 
@article{hal-01103859,
     author = {Ramachandra, K},
     title = {One more proof of Siegel's theorem},
     journal = {HAL},
     volume = {1980},
     number = {0},
     year = {1980},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01103859}
}

Ramachandra, K. One more proof of Siegel's theorem. HAL, Tome 1980 (1980) no. 0, . http://gdmltest.u-ga.fr/item/hal-01103859/