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Journal articles on the topic 'Fonctions L de Dirichlet'

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Published: 4 June 2021

Last updated: 28 January 2023

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1

Vignéras, Marie-France. "Moyennes Galoisiennes des Valeurs de Fonctions L." Canadian Journal of Mathematics 41, no. 1 (February 1, 1989): 1–13. http://dx.doi.org/10.4153/cjm-1989-001-x.

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On se propose d'étendre un résultat de Rorhlich [5] concernant les moyennes galoisiennes des valeurs en s = 1 des fonctions L associées à une forme modulaire de poids 2, tordue par certains caractères de Dirichlet. On considérera une représentation automorphe parabolique π de GL(n), n≦2, sur un corps de nombres K, et l'on s'intéressera aux valeurs des fonctions L(S,πχ) et de leurs dérivées L(m)(s, πχ), m ≧1, où χ parcourt certains caractères de Hecke de K, d'ordre fini, et où s appartient à la bande a < Re s < 1 — a, où a mesure la déviation de n par rapport à la conjecture de Petersson généralisée.

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2

Louboutin, Stéphane. "Quelques Formules Exactes Pour des Moyennes de Fonctions L de Dirichlet." Canadian Mathematical Bulletin 36, no. 2 (June 1, 1993): 190–96. http://dx.doi.org/10.4153/cmb-1993-028-8.

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RésuméNous donnons une expression finie pour la valeur L(1, X) dès lors que X est un caractère de Dirichlet modulo f ≥ 2, impair et non principal. Cette expression, valable même lorsque ce caractère n'est pas primitif, nous permet de généraliser au théorème 2 le résultat de H. Walum sur un comportement en moyenne de ces fonctions L (sa démonstration qui fait usage de sommes de Gauss ne semble pas pouvoir être adaptée au cas de caractères non primitifs.) Nous appliquons ces résultats à l'obtention de bornes pour le nombre de classes relatif des corps cyclotomiques: nous retrouvons celles de T. Metsänkylä et de K. Feng par une méthode nous permettant de les ensuite amender.

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3

Barrucand, Pierre, and Stéphane Louboutin. "Minoration au point des fonctions L attachées à des caractères de Dirichlet." Colloquium Mathematicum 65, no. 2 (1993): 301–6. http://dx.doi.org/10.4064/cm-65-2-301-306.

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4

Louboutin, Stéphane. "Corrections à: Quelques Formules Exactes Pour des Moyennes de Fonctions L de Dirichlet." Canadian Mathematical Bulletin 37, no. 1 (March 1, 1994): 89. http://dx.doi.org/10.4153/cmb-1994-013-0.

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5

Burnol, Jean-François. "Sur certains espaces de Hilbert de fonctions entières, liés à la transformation de Fourier et aux fonctions L de Dirichlet et de Riemann." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 333, no. 3 (August 2001): 201–6. http://dx.doi.org/10.1016/s0764-4442(01)02036-5.

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6

Minh, Hoang Ngoc. "Fonctions de Dirichlet d'ordre n et de paramètre t." Discrete Mathematics 180, no. 1-3 (February 1998): 221–41. http://dx.doi.org/10.1016/s0012-365x(97)00117-9.

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7

Michel, Philippe. "Sur les zéros de fonctions L sur les corps de fonctions." Mathematische Annalen 313, no. 2 (February 1, 1999): 359–70. http://dx.doi.org/10.1007/s002080050264.

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8

Bogdan, Krzysztof, and Tomasz Jakubowski. "Problème de Dirichlet pour les fonctions \alpha -harmoniques sur les domaines coniques." Annales mathématiques Blaise Pascal 12, no. 2 (2005): 297–308. http://dx.doi.org/10.5802/ambp.208.

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9

Buchwalter, Henri. "Les fonctions de L�vy existent!" Mathematische Annalen 274, no. 1 (March 1986): 31–34. http://dx.doi.org/10.1007/bf01458015.

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10

Khan, Rizwanur, and Hieu Ngo. "Nonvanishing of Dirichlet L-functions." Algebra & Number Theory 10, no. 10 (December 9, 2016): 2081–91. http://dx.doi.org/10.2140/ant.2016.10.2081.

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11

Balasubramanian, R., and V. Kumar Murty. "Zeros of Dirichlet $L$-functions." Annales scientifiques de l'École normale supérieure 25, no. 5 (1992): 567–615. http://dx.doi.org/10.24033/asens.1660.

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12

Garunkštis, R., J. Kalpokas, and J. Steuding. "Sum of the Dirichlet L-functions over nontrivial zeros of another Dirichlet L-function." Acta Mathematica Hungarica 128, no. 3 (June 4, 2010): 287–98. http://dx.doi.org/10.1007/s10474-009-9190-y.

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13

Rane, V. V. "Dirichlet expression for L(1, χ) with general Dirichlet character." Proceedings - Mathematical Sciences 120, no. 1 (February 2010): 7–9. http://dx.doi.org/10.1007/s12044-010-0003-6.

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14

Pestour, Michel. "Valeurs en s=1 de fonctions L." Acta Arithmetica 78, no. 4 (1997): 367–76. http://dx.doi.org/10.4064/aa-78-4-367-376.

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15

Soulé, Christophe. "Sur les zéros des fonctions L automorphes." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 328, no. 11 (June 1999): 955–58. http://dx.doi.org/10.1016/s0764-4442(99)80304-8.

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16

GARUNKŠTIS, RAMŪNAS, and JUSTAS KALPOKAS. "THE DISCRETE MEAN SQUARE OF THE DIRICHLET L-FUNCTION AT NONTRIVIAL ZEROS OF ANOTHER DIRICHLET L-FUNCTION." International Journal of Number Theory 09, no. 04 (May 7, 2013): 945–63. http://dx.doi.org/10.1142/s1793042113500085.

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17

Funakura, Takeo. "On Coefficients of Artin L Functions as Dirichlet Series." Canadian Mathematical Bulletin 33, no. 1 (March 1, 1990): 50–54. http://dx.doi.org/10.4153/cmb-1990-008-1.

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AbstractThe paper is motivated by a result of Ankeny [1] above Dirichlet L functions in 1952. We generalize this from Dirichlet L functions to Artin L functions of relative abelian extensions, by complementing the ingenious proof of Ankeny's theorem given by Iwasaki [4]. Moreover, we characterize Dirichlet L functions in the class of all Artin L functions in terms of coefficients as Dirichlet series.

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18

Funakura, Takeo. "On characterization of Dirichlet L-functions." Acta Arithmetica 76, no. 4 (1996): 305–15. http://dx.doi.org/10.4064/aa-76-4-305-315.

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19

Mittou, Brahim, and Abdallah Derbal. "Method for calculating Dirichlet L-functions." Mathematica Montisnigri 54 (2022): 51–58. http://dx.doi.org/10.20948/mathmontis-2022-54-5.

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Recently, the authors gave asymptotic formulas for L(s, χ), which associated with a primitive Dirichlet character χ, in terms of the generalized Bernoulli numbers. In this paper, based on the aforementioned asymptotic formulas we describe a method for calculating Dirichlet L-functions that can be used to validate the generalized Riemann hypothesis up to a height T > 0. Our method is a refinement of the one presented by Davies and Haselgrove.

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20

Fujii, Akio. "Zeta zeros and Dirichlet $L$-functions." Proceedings of the Japan Academy, Series A, Mathematical Sciences 64, no. 6 (1988): 215–18. http://dx.doi.org/10.3792/pjaa.64.215.

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21

Hu, Pei-Chu, and Ai-Di Wu. "Zero distribution of Dirichlet L-functions." Annales Academiae Scientiarum Fennicae Mathematica 41 (2016): 775–88. http://dx.doi.org/10.5186/aasfm.2016.4152.

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22

Heath-Brown, D. R. "Fractional moments of Dirichlet L-functions." Acta Arithmetica 145, no. 4 (2010): 397–409. http://dx.doi.org/10.4064/aa145-4-5.

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23

Kim, Jae Moon. "Formal groups and dirichlet L-functions." Journal of Number Theory 37, no. 2 (February 1991): 161–67. http://dx.doi.org/10.1016/s0022-314x(05)80033-2.

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24

Garunkštis, Ramūnas. "Self-approximation of Dirichlet L-functions." Journal of Number Theory 131, no. 7 (July 2011): 1286–95. http://dx.doi.org/10.1016/j.jnt.2011.01.013.

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25

Eminyan, K. M. "?-Universality of the Dirichlet L-function." Mathematical Notes of the Academy of Sciences of the USSR 47, no. 6 (June 1990): 618–22. http://dx.doi.org/10.1007/bf01170896.

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26

Friedlander, J. B., and H. Iwaniec. "A note on Dirichlet L-functions." Expositiones Mathematicae 36, no. 3-4 (December 2018): 343–50. http://dx.doi.org/10.1016/j.exmath.2018.06.003.

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27

Dixit, Atul, Arindam Roy, and Alexandru Zaharescu. "Monotonicity results for Dirichlet L -functions." Journal of Mathematical Analysis and Applications 410, no. 1 (February 2014): 307–15. http://dx.doi.org/10.1016/j.jmaa.2013.08.031.

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28

Peter, Manfred. "Mean values of Dirichlet L-series." Mathematische Annalen 318, no. 1 (September 1, 2000): 67–84. http://dx.doi.org/10.1007/s002080000109.

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29

Heim, Bernhard E. "Quotients of L-functions." Nagoya Mathematical Journal 160 (2000): 143–59. http://dx.doi.org/10.1017/s002776300000773x.

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AbstractIn this paper a certain type of Dirichlet series, attached to a pair of Jacobi forms and Siegel modular forms is studied. It is shown that this series can be analyzed by a new variant of the Rankin-Selberg method. We prove that for eigenforms the Dirichlet series have an Euler product and we calculate all the local L-factors. Globally this Euler product is essentially the quotient of the standard L-functions of the involved Jacobi- and Siegel modular form.

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30

DJANKOVIĆ, GORAN. "THE RECIPROCITY LAW FOR THE TWISTED SECOND MOMENT OF DIRICHLET -FUNCTIONS OVER RATIONAL FUNCTION FIELDS." Bulletin of the Australian Mathematical Society 98, no. 3 (August 28, 2018): 383–88. http://dx.doi.org/10.1017/s0004972718000874.

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We prove the reciprocity law for the twisted second moments of Dirichlet $L$-functions over rational function fields, corresponding to two irreducible polynomials. This formula is the analogue of the formulas for Dirichlet $L$-functions over $\mathbb{Q}$ obtained by Conrey [‘The mean-square of Dirichlet $L$-functions’, arXiv:0708.2699 [math.NT] (2007)] and Young [‘The reciprocity law for the twisted second moment of Dirichlet $L$-functions’, Forum Math. 23(6) (2011), 1323–1337].

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31

Mínguez, Alberto. "Fonctions zêta ℓ-modulaires." Nagoya Mathematical Journal 208 (December 2012): 39–65. http://dx.doi.org/10.1017/s0027763000010588.

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AbstractLet F be a non-Archimedean locally compact field, of residual characteristic p, and let D be a finite-dimensional central division F-algebra. Let ℓ be a prime number different from p. In this article, generalizing the results of [GJ], we associate, to each ℓ-modular smooth irreducible representation π of GLm(D), two invariants L(T,π), ε(T,π,ψ), where T is an indeterminate and ψ is a nontrivial character of F.

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32

Royer, E. "Petits zéros de fonctions L de formes modulaires." Acta Arithmetica 99, no. 2 (2001): 147–72. http://dx.doi.org/10.4064/aa99-2-3.

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33

Lafforgue, Vincent. "Valeurs spéciales des fonctions L en caractéristique p." Journal of Number Theory 129, no. 10 (October 2009): 2600–2634. http://dx.doi.org/10.1016/j.jnt.2009.04.002.

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34

Cassou-Noguès, Philippe, and Martin J. Taylor. "Espaces homogènes principaux, unités elliptiques et fonctions $L $." Annales de l’institut Fourier 44, no. 3 (1994): 631–61. http://dx.doi.org/10.5802/aif.1413.

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35

Mœglin, C. "Fonctions L de paires pour les groupes classiques." Ramanujan Journal 28, no. 2 (April 27, 2012): 187–209. http://dx.doi.org/10.1007/s11139-012-9372-z.

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36

Katsurada, Masanori, and Kohji Matsumoto. "The mean values of Dirichlet L-functions at integer points and class numbers of cyclotomic fields." Nagoya Mathematical Journal 134 (June 1994): 151–72. http://dx.doi.org/10.1017/s0027763000004906.

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Let q be a positive integer, and L(s, χ) the Dirichlet L-function corresponding to a Dirichlet character χ mod q. We putwhere χ runs over all Dirichlet characters mod q except for the principal character χ0.

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37

Van Order, Jeanine. "Dirichlet twists of GL n -automorphic L-functions and hyper-Kloosterman Dirichlet series." Annales de la Faculté des sciences de Toulouse : Mathématiques 30, no. 3 (October 26, 2021): 633–703. http://dx.doi.org/10.5802/afst.1687.

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38

MOURTADA, M., and V. KUMAR MURTY. "OMEGA THEOREMS FOR $\frac{L'}{L}(1, \chi_D)$." International Journal of Number Theory 09, no. 03 (April 7, 2013): 561–81. http://dx.doi.org/10.1142/s1793042112501485.

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A classical result of Chowla [Improvement of a theorem of Linnik and Walfisz, Proc. London Math. Soc. (2) 50 (1949) 423–429 and The Collected Papers of Sarvadaman Chowla, Vol. 2 (Centre de Recherches Mathematiques, 1999), pp. 696–702] states that for infinitely many fundamental discriminants D we have [Formula: see text] where χD is the quadratic Dirichlet character of conductor D. In this paper, we prove an analogous result for the logarithmic derivative [Formula: see text], and investigate the growth of the logarithmic derivatives of real Dirichlet L-functions. We show that there are infinitely many fundamental discriminants D (both positive and negative) such that [Formula: see text] and infinitely many fundamental discriminants 0 < D such that [Formula: see text] In particular, we show that the Euler–Kronecker constant γK of a quadratic field K satisfies γK = Ω( log log |dK|). We get sharper results assuming the GRH. Moreover, we evaluate the moments of [Formula: see text].

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39

Ma, Rong, Yana Niu, and Yulong Zhang. "On asymptotic properties of the generalized Dirichlet L-functions." International Journal of Number Theory 15, no. 06 (July 2019): 1305–21. http://dx.doi.org/10.1142/s1793042119500738.

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Let [Formula: see text] be an integer, [Formula: see text] denote a Dirichlet character modulo [Formula: see text], for any real number [Formula: see text], we define the generalized Dirichlet [Formula: see text]-functions [Formula: see text] where [Formula: see text] with [Formula: see text] and [Formula: see text] both real. It can be extended to all [Formula: see text] by analytic continuation. In this paper, we study the mean value properties of the generalized Dirichlet [Formula: see text]-functions, and obtain several sharp asymptotic formulae by using analytic method.

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40

Xu, Zhefeng, and Wenpeng Zhang. "Some identities involving the Dirichlet L-function." Acta Arithmetica 130, no. 2 (2007): 157–66. http://dx.doi.org/10.4064/aa130-2-5.

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41

Young, Matthew. "The fourth moment of Dirichlet $L$-functions." Annals of Mathematics 173, no. 1 (January 4, 2011): 1–50. http://dx.doi.org/10.4007/annals.2011.173.1.1.

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42

Fujii, Akio. "Zeta zeros and Dirichlet $L$-functions, II." Proceedings of the Japan Academy, Series A, Mathematical Sciences 64, no. 8 (1988): 296–99. http://dx.doi.org/10.3792/pjaa.64.296.

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43

LOUBOUTIN, STEPHANE R. "TWISTED QUADRATIC MOMENTS FOR DIRICHLET L-FUNCTIONS." Bulletin of the Korean Mathematical Society 52, no. 6 (November 30, 2015): 2095–105. http://dx.doi.org/10.4134/bkms.2015.52.6.2095.

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44

Balčiūnas, Aidas, and Antanas Laurinčikas. "The Laplace transform of Dirichlet L-functions." Nonlinear Analysis: Modelling and Control 17, no. 2 (April 25, 2012): 127–38. http://dx.doi.org/10.15388/na.17.2.14063.

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45

Li, H. "Zero-free regions for Dirichlet L-functions." Quarterly Journal of Mathematics 50, no. 197 (March 1, 1999): 13–23. http://dx.doi.org/10.1093/qjmath/50.197.13.

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46

Wang, Nianliang, Junzhuang Li, and Duansen Liu. "Euler numbers congruences and Dirichlet L-functions." Journal of Number Theory 129, no. 6 (June 2009): 1522–31. http://dx.doi.org/10.1016/j.jnt.2009.01.004.

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47

Childress, Nancy, and Jeffrey Stopple. "Formal groups and Dirichlet L-functions, I." Journal of Number Theory 41, no. 3 (July 1992): 283–94. http://dx.doi.org/10.1016/0022-314x(92)90127-b.

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48

Childress, Nancy, and Jeffrey Stopple. "Formal groups and Dirichlet L-functions, II." Journal of Number Theory 41, no. 3 (July 1992): 295–302. http://dx.doi.org/10.1016/0022-314x(92)90128-c.

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49

Conrey, J. B., and K. Soundararajan. "Real zeros of quadratic Dirichlet L-functions." Inventiones mathematicae 150, no. 1 (October 2002): 1–44. http://dx.doi.org/10.1007/s00222-002-0227-x.

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50

Chandee, Vorrapan, and Xiannan Li. "The eighth moment of Dirichlet L -functions." Advances in Mathematics 259 (July 2014): 339–75. http://dx.doi.org/10.1016/j.aim.2014.03.020.

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