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2014 | 12 | 6 | 848-860
Tytuł artykułu

Upper bounds for the moments of derivatives of Dirichlet L-functions

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
In this paper, we give certain upper bounds for the 2k-th moments, k ≥ 1/2, of derivatives of Dirichlet L-functions at s = 1/2 under the assumption of the Generalized Riemann Hypothesis.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
6
Strony
848-860
Opis fizyczny
Daty
wydano
2014-06-01
online
2014-03-19
Twórcy
autor
Bibliografia
  • [1] Bui H.M., Milinovich M.B., Central values of derivatives of Dirichlet L-functions, Int. J. Number Theory, 2011, 7(2), 371–388 http://dx.doi.org/10.1142/S1793042111004125
  • [2] Chandee V., Explicit upper bounds for L-functions on the critical line, Proc. Amer. Math. Soc., 2009, 137(12), 4049–4063 http://dx.doi.org/10.1090/S0002-9939-09-10075-8
  • [3] Chandee V., Li X., Lower bounds for small fractional moments of Dirichlet L-functions, Int. Math. Res. Not. IMRN, 2013, 19, 4349–4381
  • [4] Conrey J.B., The fourth moment of derivatives of the Riemann zeta-function, Quart. J. Math. Oxford, 1988, 39(153), 21–36 http://dx.doi.org/10.1093/qmath/39.1.21
  • [5] Davenport H., Multiplicative Number Theory, 3rd ed., Grad. Texts in Math., 74, Springer, New York, 2000
  • [6] Heath-Brown D.R., The fourth power mean of Dirichlet’s L-functions, Analysis, 1981, 1(1), 25–32 http://dx.doi.org/10.1524/anly.1981.1.1.25
  • [7] Heath-Brown D.R., Fractional moments of Dirichlet L-functions, Acta Arith., 2010, 145(4), 397–409 http://dx.doi.org/10.4064/aa145-4-5
  • [8] Koltes T., Soundararajan’s Upper Bound on Moments of the Riemann Zeta Function, Bachelor thesis, Swiss Federal Institute of Technology Zürich, Switzerland, 2010
  • [9] Michel P., VanderKam J., Non-vanishing of high derivatives of Dirichlet L-functions at the central point, J. Number Theory, 2000, 81(1), 130–148 http://dx.doi.org/10.1006/jnth.1999.2460
  • [10] Milinovich M.B., Upper bounds for moments of ζ′(ρ), Bull. Lond. Math. Soc., 2010, 42(1), 28–44 http://dx.doi.org/10.1112/blms/bdp096
  • [11] Milinovich M.B., Moments of the Riemann zeta-function at its relative extrema on the critical line, Bull. Lond. Math. Soc., 2011, 43(6), 1119–1129 http://dx.doi.org/10.1112/blms/bdr047
  • [12] Paley R.E.A.C., On the k-analogues of some theorems in the theory of the Riemann ζ-function, Proc. Lond. Math. Soc., 1931, 32, 273–311 http://dx.doi.org/10.1112/plms/s2-32.1.273
  • [13] Radziwiłł M., The 4.36th moment of the Riemann zeta-function, Int. Math. Res. Not. IMRN, 2012, 18, 4245–4259
  • [14] Rudnick Z., Soundararajan K., Lower bounds for moments of L-functions, Proc. Natl. Acad. Sci. USA, 2005, 102(19), 6837–6838 http://dx.doi.org/10.1073/pnas.0501723102
  • [15] Sono K., Lower bounds for the moments of the derivatives of the Riemann zeta-function and Dirichlet L-functions, Lith. Math. J., 2012, 52(4), 420–434 http://dx.doi.org/10.1007/s10986-012-9184-2
  • [16] Soundararajan K., The fourth moment of Dirichlet L-functions, In: Analytic Number Theory, Göttingen, June 20–24, 2005, Clay Math. Proc., 7, American Mathematical Society, Providence, 2007, 239–246
  • [17] Soundararajan K., Moments of the Riemann zeta function, Ann. of Math., 2009, 170(2), 981–993 http://dx.doi.org/10.4007/annals.2009.170.981
  • [18] Young M.P., The fourth moment of Dirichlet L-functions, Ann. of Math., 2011, 173(1), 1–50 http://dx.doi.org/10.4007/annals.2011.173.1.1
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0382-x
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