On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 142, Issue 3, 2007, Pages 395-405

  Tsumura, Hirofumi ^a  

^a TOKYO METROPOLITAN UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34249670323     PISSN: 03050041     EISSN: 14698064     Source Type: Journal    
DOI: 10.1017/S0305004107000059     Document Type: Article

References (12)

1. A. ERDELYI (Dir.), W. MAGNUS, F. OBERTHETTINGER AND F. TRICOMI. Higher Transcendental Functions. Vol. 1 (McGraw-Hill, 1953).
2. J. G. HUARD, K. S. WILLIAMS AND NAN-Y UE ZHANG. On Tornheim's double series. Acta Arith. 75 (1996), 105-117.
3. K. MATSUMOTO. On the analytic continuation of various multiple zeta-functions. Number Theory for the Millennium II, Proc. of the Millennial Conference on Number Theory, M. A. Bennett et al. (eds.) (A. K. Peters, 2002), 417-440.
4. K. MATSUMOTO. On Mordell-Tornheim and other multiple zeta-functions. Proceedings of the Session in analytic number theory and Diophantine equations (Bonn, January-June 2002), D. R. Heath-Brown and B. Z. Moroz (eds.). Bonner Mathematische Schriften Nr. 360 (Bonn, 2003), n. 25, 17 pp.
5. K. MATSUMOTO. Functional equations for double zeta-functions. Math. Proc. Camb. Phil. Soc. 136 (2004), 1-7.
6. L. J. MORDELL. On the evaluation of some multiple series. J. London Math. Soc. 33 (1958), 368-371.
7. M. V. SUBBARAO AND R. SITARAMACHANDRARAO. On some infinite series of L. J. Mordell and their analogues. Pacific J. Math. 119 (1985), 245-255.
8. L. TORNHEIM. Harmonic double series. Amer. J. Math. 72 (1950), 303-314.
9. H. TSUMURA. On some combinatorial relations for Tornheim's double series. Acta Arith. 105 (2002), 239-252.
10. H. TSUMURA. On alternating analogues of Tornheim's double series. Proc. Amer. Math. Soc. 131 (2003), 3633-3641.
11. H. TSUMURA. Certain functional relations for the double harmonic series related to the double Euler numbers. J. Austral. Math. Soc., Ser. A. 79 (2005), 319-333.
12. D. ZAGIER. Values of zeta functions and their applications. Proc. First Congress of Math. Paris, vol. II (Birkhäuser Verlag, 1994), 497-512.