A functional relation for the Tornheim double zeta function

Acta Arithmetica

Volumn 125, Issue 3, 2006, Pages 257-263

  Nakamura, Takashi ^a,b  

^a Nagoya University ^*

^b NAGOYA UNIVERSITY   (Japan)

Author keywords

Euler Zagier double zeta function; Tornheim double zeta function

Indexed keywords

EID: 33845586284     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa125-3-3     Document Type: Article

References (11)

1. T. M. Apostol, Introduction to Analytic Number Theory, Springer, 1976.
2. O. Espinosa and V. H. Moll, The evaluation of Tornheim double sums. I, J. Number Theory 116 (2006), 200-229.
3. J. G. Huard, K. S. Williams, and Z. Y. Zhang, On Tornheim's double series, Acta Arith. 75 (1996), 105-117.
4. K. Matsumoto, On the analytic continuation of various multiple zeta-functions, in: Number Theory for the Millennium, II (Urbana, IL, 2000), M. A. Bennett et al. (eds.), A K Peters, 2002, 417-440.
5. L. J. Mordell, On the evaluation of some multiple series, J. London Math. Soc. 33 (1958), 368-371.
6. M. V. Subbarao and R. Sitaramachandrarao, On some infinite series of L. J. Mordell and their analogues, Pacific J. Math. 119 (1985), 245-255.
7. L. Tornheim, Harmonic double series, Amer. J. Math. 72 (1950), 303-314.
8. H. Tsumura, On some combinatorial relations for Tornheim's double series, Acta Arith. 105 (2002), 239-252.
9. -, On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function, Math. Proc. Cambridge Philos. Soc., to appear; Tokyo Metropolitan Univ. Preprint Ser., 2006, No. 2, 11 pp.
10. D. Zagier, Values of zeta functions and their applications, in: First European Congress of Mathematics, Vol. II (Paris, 1992), Progr. Math. 120, Birkhäuser, 1994, 497-512.
11. -, Introduction to multiple zeta values, lectures at Kyushu Univ., 1999.