Ordre de grandeur de L ( 1 , χ ) et de L ' ( 1 , χ )

Jean-René Joly; Claude Moser

Annales de l'institut Fourier (1979)

  • Volume: 29, Issue: 1, page 125-135
  • ISSN: 0373-0956

Abstract

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The paper gives a rough description of the distribution of values of L ' ( 1 , χ ) ( χ , a real primitive residue character), which usually lie under π 2 / 6 ; and a proof of the following theorem: if L ' ( 1 , χ ) < ( π 2 / 6 ) - ϵ , then L ( 1 , χ ) > c ( ϵ ) / log k ( k the conductor of χ ; c ( ϵ ) , a positive, computable constant.

How to cite

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Joly, Jean-René, and Moser, Claude. "Ordre de grandeur de $L(1,\chi )$ et de $L^{\prime }(1,\chi )$." Annales de l'institut Fourier 29.1 (1979): 125-135. <http://eudml.org/doc/74390>.

@article{Joly1979,
abstract = {On étudie sommairement la distribution des valeurs de $L^\{\prime \}(1,\chi )$ ($\chi $ : caractère de Dirichlet primitif réel) et on constate qu’on a en général $L^\{\prime \}(1,\chi ) &lt; \pi ^2/6$; on démontre par ailleurs que si $L^\{\prime \}(1,\chi ) &lt; (\pi ^2/6) - \varepsilon $, alors$L(1,\chi ) &gt; c(\varepsilon ) / \log k$ ($k$ : conducteur de $\chi $; $c(\varepsilon )$: constante positive effectivement calculable.},
author = {Joly, Jean-René, Moser, Claude},
journal = {Annales de l'institut Fourier},
keywords = {distribution of values},
language = {fre},
number = {1},
pages = {125-135},
publisher = {Association des Annales de l'Institut Fourier},
title = {Ordre de grandeur de $L(1,\chi )$ et de $L^\{\prime \}(1,\chi )$},
url = {http://eudml.org/doc/74390},
volume = {29},
year = {1979},
}

TY - JOUR
AU - Joly, Jean-René
AU - Moser, Claude
TI - Ordre de grandeur de $L(1,\chi )$ et de $L^{\prime }(1,\chi )$
JO - Annales de l'institut Fourier
PY - 1979
PB - Association des Annales de l'Institut Fourier
VL - 29
IS - 1
SP - 125
EP - 135
AB - On étudie sommairement la distribution des valeurs de $L^{\prime }(1,\chi )$ ($\chi $ : caractère de Dirichlet primitif réel) et on constate qu’on a en général $L^{\prime }(1,\chi ) &lt; \pi ^2/6$; on démontre par ailleurs que si $L^{\prime }(1,\chi ) &lt; (\pi ^2/6) - \varepsilon $, alors$L(1,\chi ) &gt; c(\varepsilon ) / \log k$ ($k$ : conducteur de $\chi $; $c(\varepsilon )$: constante positive effectivement calculable.
LA - fre
KW - distribution of values
UR - http://eudml.org/doc/74390
ER -

References

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  1. [1] S. CHOWLA, Improvement of a result of Linnik and Walfisz, Proc. London Math. Soc., 50 (1949), 423-429. Zbl0032.11006MR10,285d
  2. [2] S. CHOWLA, On the class number of the corpus P(√—k), Proc. Nat. Inst. Sc. India, 13 (1947), 197-200. 
  3. [3] H. DAVENPORT, Multiplicative number theory, Markham, Chicago (1967). Zbl0159.06303MR36 #117
  4. [4] P.D.T.A. ELLIOTT, On the size of L(1,χ), J. reine angew Math., 236 (1969), 26-36. Zbl0175.04302MR40 #2619
  5. [5] W. FLUCH, Zur Abschätzung von L(1,χ), Nachr. Akad. Wiss. Göttingen Math. Phys., (1964), 101-102. Zbl0121.28401MR29 #4741
  6. [6] J.R. JOLY, Suites périodiques et inégalité de Polya, Bull. Sc. Math., 102 (1978), 3-13. Zbl0384.10019MR58 #5545
  7. [7] P.T. JOSHI, The size of L(1,χ) for real characters χ with prime modulus, J. Number Theory, 2 (1970), 58-73. Zbl0208.31103MR40 #4215
  8. [8] J. PINTZ, Elementary methods in the theory of L-functions, II, Acta Arithm., 31 (1976), 273-289. Zbl0307.10041MR56 #2936
  9. [9] J.E. LITTLEWOOD, On the class number of the corpus P(√—k), Proc. London Math. Soc., 28 (1927), 358-372. Zbl54.0206.02JFM54.0206.02
  10. [10] C. MOSER, Distribution des valeurs de L'(1,χ), Sém. Th. Nombres, Grenoble. 
  11. [11] D. SHANKS, Littlewood bounds, Proc. Symp. Pure Math. A.M.S., Analytic Number Theory, XXIV (1973). 

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