On the singularities of multiple L-functions
Alexandru Zaharescu ; Mohammad Zaki
Open Mathematics, Tome 8 (2010), p. 289-298 / Harvested from The Polish Digital Mathematics Library

We investigate the singularities of a class of multiple L-functions considered by Akiyama and Ishikawa [2].

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:269072
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     author = {Alexandru Zaharescu and Mohammad Zaki},
     title = {On the singularities of multiple L-functions},
     journal = {Open Mathematics},
     volume = {8},
     year = {2010},
     pages = {289-298},
     zbl = {1203.11060},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0004-9}
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Alexandru Zaharescu; Mohammad Zaki. On the singularities of multiple L-functions. Open Mathematics, Tome 8 (2010) pp. 289-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0004-9/

[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 | Zbl 0972.11085

[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 | Zbl 1028.11058

[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 | Zbl 0036.18603

[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 | Zbl 1031.11051

[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 | Zbl 1056.11049

[8] Matsumoto K., Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series, Nagoya Math. J., 2003, 172, 59–102 | Zbl 1060.11053

[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 | Zbl 0903.11021

[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 | Zbl 1195.11119

[11] Matsumoto K., Analytic properties of multiple zeta-functions in several variables, Number theory, 153–173, Dev. Math., 15, Springer, New York, 2006 | Zbl 1197.11120

[12] Matsumoto K., Tsumura H., On Witten multiple zeta-functions associated with semisimple Lie algebras I, Ann. Inst. Fourier (Grenoble), 2006, 56, 1457–1504 | Zbl 1168.11036

[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 | Zbl 1151.11045

[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 | Zbl 0081.27501

[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 | Zbl 1124.11046

[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 | Zbl 1153.11047

[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 | Zbl 1010.11048

[19] Tsumura H.,Combinatorial relations for Euler-Zagier sums, Acta Arith., 2004, 111, 27–42 | Zbl 1153.11327

[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 | Zbl 1097.11048

[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 | Zbl 1149.11044

[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 | Zbl 0822.11001

[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 | Zbl 0949.11042