Certain functional relations for the double harmonic series related to the double Euler numbers

Journal of the Australian Mathematical Society

Volumn 79, Issue 3, 2005, Pages 319-333

  Tsumura, Hirofumi ^a  

^a TOKYO METROPOLITAN UNIVERSITY   (Japan)

Author keywords

Double Euler numbers; Double harmonic series; Mordell Tornheim double zeta functions; Riemann zeta function; Uniformly convergent series

Indexed keywords

EID: 31144448131     PISSN: 14467887     EISSN: None     Source Type: Journal    
DOI: 10.1017/S1446788700010922     Document Type: Article

References (11)

1. K. Dilcher, Zeros of Bernoulli, generalized Bernoulli and Euler polynomials, Mem. Amer. Math. Soc. 386 (Amer. Math. Soc., Providence, RI, 1988).
2. J. G. Huard, K. S. Williams and Z. Nan-Yue, 'On Tornheim's double series', Acta Arith. 75 (1996), 105-117.
3. K. Matsumoto, 'On Mordell-Tornheim and other multiple zeta-functions', in: Proceedings of the Session in analytic number theory and Diophantine equations. Bonn, January-June 2002 (eds. D. R. Heath-Brown and B. Z. Moroz), Bonner Mathematische Schriften 360 (Bonn, 2003) pp. 17.
4. L. J. Mordell, 'On the evaluation of some multiple series', J. London Math. Soc. 33 (1958), 368-371.
5. M. V. Subbarao and R. Sitaramachandrarao, 'On some infinite series of L. J. Mordell and their analogues', Pacific J. Math. 119 (1985), 245-255.
6. L. Tornheim, 'Harmonie double series', Amer. J. Math. 72 (1950), 303-314.
7. H. Tsumura, 'On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function', preprint.
8. _, 'On some combinatorial relations for Tornheim's double series', Acta Arith. 105 (2002), 239-252.
9. _, 'On alternating analogues of Tornheim's double series', Proc. Amer. Math. Soc. 131 (2003), 3633-3641.
10. _, 'Multiple harmonic series related to multiple Euler numbers', J. Number Theory 106 (2004), 155-168.
11. L. C. Washington, Introduction to the cyclotomic fields, 2nd edition (Springer, New York, 1997).