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2010 | 8 | 2 | 289-298
Tytuł artykułu

On the singularities of multiple L-functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the singularities of a class of multiple L-functions considered by Akiyama and Ishikawa [2].
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
2
Strony
289-298
Opis fizyczny
Daty
wydano
2010-04-01
online
2010-04-14
Twórcy
Bibliografia
  • [1] Akiyama S., Egami S., Tanigawa Y., Analytic continuation of multiple zeta-functions and their values at non-positive integers, Acta Arith., 2001, 98, 107–116 http://dx.doi.org/10.4064/aa98-2-1
  • [2] Akiyama S., Ishikawa H., On analytic continuation of multiple L-functions and related zeta-functions, Analytic number theory (Beijing/Kyoto, 1999), 1–16, Dev. Math., 6, Kluwer Acad. Publ., Dordrecht, 2002
  • [3] Apostol T., Vu T.H., Dirichlet series related to the Riemann zeta function, J. Number Theory, 1984, 19, 85–102 http://dx.doi.org/10.1016/0022-314X(84)90094-5
  • [4] Atkinson F.V., The mean value of the Riemann zeta function, Acta Math., 1949, 81, 353–376 http://dx.doi.org/10.1007/BF02395027
  • [5] Hardy G.H., Notes on some points in the integral calculus LV, On the integration of Fourier series, Messenger of Math., 1922, 51, 186–192; reprinted in Collected Papers of Hardy G.H. (including joint papers with Littlewood J.E. and others), Clarendon Press, Oxford, 1969, III, 506–512
  • [6] Matsumoto K., On the analytic continuation of various multiple zeta-functions, Number theory for the millennium, II (Urbana, IL, 2000), 417–440, A K Peters, Natick, MA, 2002
  • [7] Matsumoto K., On Mordell-Tornheim and other multiple zeta-functions, Proceedings of the Session in Analytic Number Theory and Diophantine Equations, 17 pp., Bonner Math. Schriften, 360, Univ. Bonn, Bonn, 2003
  • [8] Matsumoto K., Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series, Nagoya Math. J., 2003, 172, 59–102
  • [9] Matsumoto K., Asymptotic series for double zeta, double gamma, and Hecke L-functions, Math. Proc. Cambridge Phil. Soc., 1998, 123, 385–405 http://dx.doi.org/10.1017/S0305004197002168
  • [10] Matsumoto K., The analytic continuation and the asymptotic behaviour of certain multiple zeta-functions II, Analytic and probabilistic methods in number theory (Palanga, 2001), 188–194, TEV, Vilnius, 2002
  • [11] Matsumoto K., Analytic properties of multiple zeta-functions in several variables, Number theory, 153–173, Dev. Math., 15, Springer, New York, 2006
  • [12] Matsumoto K., Tsumura H., On Witten multiple zeta-functions associated with semisimple Lie algebras I, Ann. Inst. Fourier (Grenoble), 2006, 56, 1457–1504
  • [13] Matsumoto K., Tsumura H., Functional relations for various multiple zeta-functions, Analytic Number Theory (Kyoto, 2005), RIMS Kokyuroku, 2006, 1512, 179–190
  • [14] Matsumoto K., Tsumura H., A new method of producing functional relations among multiple zeta-functions, Quart. J. Math., 2008, 59, 55–83 http://dx.doi.org/10.1093/qmath/ham025
  • [15] Mordell L.J., On the evaluation of some multiple series, J. London Math. Soc., 1958, 33, 368–371 http://dx.doi.org/10.1112/jlms/s1-33.3.368
  • [16] Murty R., Sinha K., Multiple Hurwitz zeta functions, Multiple Dirichlet series, automorphic forms, and analytic number theory, 135–156, Proc. Sympos. Pure Math., 75, Amer. Math. Soc., Providence, RI, 2006
  • [17] Nakamura T., A functional relation for the Tornheim double zeta function, Acta Arith., 2006, 125, 257–263 http://dx.doi.org/10.4064/aa125-3-3
  • [18] Tsumura H., On some combinatorial relations for Tornheim’s double series, Acta Arith., 2002, 105, 239–252 http://dx.doi.org/10.4064/aa105-3-3
  • [19] Tsumura H.,Combinatorial relations for Euler-Zagier sums, Acta Arith., 2004, 111, 27–42
  • [20] Tsumura H., Certain functional relations for the double harmonic series related to the double Euler numbers, J. Aust. Math. Soc., 2005, 79(3), 319–333 http://dx.doi.org/10.1017/S1446788700010922
  • [21] Tsumura H.,On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function, Math. Proc. Cambridge Philos. Soc., 2007, 142, 395–405
  • [22] Zagier D., Values of zeta functions and their applications, First European Congress of Mathematics, Vol. II (Paris, 1992), 497–512, Progr. Math., 120, Birkhäuser, Basel, 1994
  • [23] Zhao J., Analytic continuation of multiple zeta functions, Proc. Amer. Math. Soc., 2000, 128, 1275–1283 http://dx.doi.org/10.1090/S0002-9939-99-05398-8
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0004-9
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