PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2011 | 9 | 1 | 102-126
Tytuł artykułu

An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove an explicit formula of Atkinson type for the error term in the asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. To deal with the case when coefficients of the Dirichlet polynomial are complex, we apply the idea of the first author in his study on mean values of Dirichlet L-functions.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
1
Strony
102-126
Opis fizyczny
Daty
wydano
2011-02-01
online
2010-12-30
Twórcy
Bibliografia
  • [1] Atkinson F.V., The mean-value of the Riemann zeta function, Acta Math., 1949, 81(1), 353–376 http://dx.doi.org/10.1007/BF02395027
  • [2] Balasubramanian R., Conrey J.B., Heath-Brown D.R., Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial, J. Reine Angew. Math., 1985, 357, 161–181
  • [3] Hafner J.L., Ivić A., On the mean-square of the Riemann zeta-function on the critical line, J. Number Theory, 1989, 32(2), 151–191 http://dx.doi.org/10.1016/0022-314X(89)90024-3
  • [4] Heath-Brown D.R., The mean value theorem for the Riemann zeta-function, Mathematika, 1978, 25(2), 177–184 http://dx.doi.org/10.1112/S0025579300009414
  • [5] Ishikawa H., A difference between the values of |L(1/2 + it, χ j)| and |L(1/2 + it, χ k)|. I, Comment. Math. Univ. St. Pauli, 2006, 55(1), 41–66
  • [6] Ishikawa H., A difference between the values of |L(1/2 + it, χ j)| and |L(1/2 + it, χk)|. II, Comment. Math. Univ. St. Pauli, 2007, 56(1), 1–9
  • [7] Ivić A., The Riemann Zeta-Function, Wiley-Intersci. Publ., John Wiley & Sons, New York, 1985
  • [8] Ivić A., Lectures on Mean Values of the Riemann Zeta Function, Tata Inst. Fund. Res. Lectures on Math. and Phys., 82, Springer, Berlin, 1991
  • [9] Jutila M., Transformation formulae for Dirichlet polynomials, J. Number Theory, 1984, 18(2), 135–156 http://dx.doi.org/10.1016/0022-314X(84)90049-0
  • [10] Jutila M., Lectures on a Method in the Theory of Exponential Sums, Tata Inst. Fund. Res. Lectures on Math. and Phys., 80, Springer, Berlin, 1987
  • [11] Katsurada M., Matsumoto K., Asymptotic expansions of the mean values of Dirichlet L-functions, Math. Z., 1991, 208(1), 23–39 http://dx.doi.org/10.1007/BF02571507
  • [12] Katsurada M., Matsumoto K., A weighted integral approach to the mean square of Dirichlet L-functions, In: Number Theory and its Applications, Kyoto, November 10–14, 1997, Dev. Math., 2, Kluwer, Dordrecht, 1999, 199–229
  • [13] Matsumoto K., Recent developments in the mean square theory of the Riemann zeta and other zeta-functions, In: Number Theory, Trends Math., Birkhäuser, Basel 2000, 241–286
  • [14] Matsumoto K., On the mean square of the product of ζ(s) and a Dirichlet polynomial, Comment. Math. Univ. St. Pauli, 2004, 53(1), 1–21
  • [15] Motohashi Y., A note on the mean value of the zeta and L-functions. I, Proc. Japan Acad. Ser. A Math. Sci., 1985, 61(7), 222–224 http://dx.doi.org/10.3792/pjaa.61.222
  • [16] Motohashi Y., A note on the mean value of the zeta and L-functions. V, Proc. Japan Acad. Ser. A Math. Sci., 1986, 62(10), 399–401 http://dx.doi.org/10.3792/pjaa.62.399
  • [17] Steuding J., On simple zeros of the Riemann zeta-function in short intervals on the critical line, Acta Math. Hungar., 2002, 96(4), 259–308 http://dx.doi.org/10.1023/A:1019767816190
  • [18] Titchmarsh E.C., The Theory of the Riemann Zeta-Function, Clarendon Press, Oxford, 1951
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0085-5
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.