On étudie sommairement la distribution des valeurs de ( : caractère de Dirichlet primitif réel) et on constate qu’on a en général ; on démontre par ailleurs que si , alors ( : conducteur de ; : constante positive effectivement calculable.
The paper gives a rough description of the distribution of values of (, a real primitive residue character), which usually lie under ; and a proof of the following theorem: if , then ( the conductor of ; , a positive, computable constant.
@article{AIF_1979__29_1_125_0, author = {Joly, Jean-Ren\'e and Moser, Claude}, title = {Ordre de grandeur de $L(1,\chi )$ et de $L^{\prime }(1,\chi )$}, journal = {Annales de l'Institut Fourier}, volume = {29}, year = {1979}, pages = {125-135}, doi = {10.5802/aif.730}, mrnumber = {80d:10060}, zbl = {0386.10026}, language = {fr}, url = {http://dml.mathdoc.fr/item/AIF_1979__29_1_125_0} }
Joly, Jean-René; Moser, Claude. Ordre de grandeur de $L(1,\chi )$ et de $L^{\prime }(1,\chi )$. Annales de l'Institut Fourier, Tome 29 (1979) pp. 125-135. doi : 10.5802/aif.730. http://gdmltest.u-ga.fr/item/AIF_1979__29_1_125_0/
[1] Improvement of a result of Linnik and Walfisz, Proc. London Math. Soc., 50 (1949), 423-429. | MR 10,285d | Zbl 0032.11006
,[2] On the class number of the corpus P(√—k), Proc. Nat. Inst. Sc. India, 13 (1947), 197-200.
,[3] Multiplicative number theory, Markham, Chicago (1967). | MR 36 #117 | Zbl 0159.06303
,[4] On the size of L(1,χ), J. reine angew Math., 236 (1969), 26-36. | MR 40 #2619 | Zbl 0175.04302
,[5] Zur Abschätzung von L(1,χ), Nachr. Akad. Wiss. Göttingen Math. Phys., (1964), 101-102. | MR 29 #4741 | Zbl 0121.28401
,[6] Suites périodiques et inégalité de Polya, Bull. Sc. Math., 102 (1978), 3-13. | MR 58 #5545 | Zbl 0384.10019
,[7] The size of L(1,χ) for real characters χ with prime modulus, J. Number Theory, 2 (1970), 58-73. | MR 40 #4215 | Zbl 0208.31103
,[8] Elementary methods in the theory of L-functions, II, Acta Arithm., 31 (1976), 273-289. | MR 56 #2936 | Zbl 0307.10041
,[9] On the class number of the corpus P(√—k), Proc. London Math. Soc., 28 (1927), 358-372. | JFM 54.0206.02
,[10] Distribution des valeurs de L'(1,χ), Sém. Th. Nombres, Grenoble.
,[11] Littlewood bounds, Proc. Symp. Pure Math. A.M.S., Analytic Number Theory, XXIV (1973).
,