Algebraic structures of Euler numbers
HTML articles powered by AMS MathViewer
- by I-Chiau Huang PDF
- Proc. Amer. Math. Soc. 140 (2012), 2945-2952 Request permission
Abstract:
We define a finitely generated $\mathbb {Q}$-algebra $\mathfrak {E}$ with a module structure over the universal enveloping algebra of a Lie algebra. Identities of Euler numbers are investigated using the algebraic structures of $\mathfrak {E}$.References
- Takashi Agoh and Karl Dilcher, Convolution identities and lacunary recurrences for Bernoulli numbers, J. Number Theory 124 (2007), no. 1, 105–122. MR 2320993, DOI 10.1016/j.jnt.2006.08.009
- Karl Dilcher, Sums of products of Bernoulli numbers, J. Number Theory 60 (1996), no. 1, 23–41. MR 1405723, DOI 10.1006/jnth.1996.0110
- I-C. Huang. Algebraic structures of Bernoulli numbers and polynomials. arXiv:1005.0177.
- I-Chiau Huang and Su-Yun Huang, Bernoulli numbers and polynomials via residues, J. Number Theory 76 (1999), no. 2, 178–193. MR 1684682, DOI 10.1006/jnth.1998.2364
- J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Revised edition, Graduate Studies in Mathematics, vol. 30, American Mathematical Society, Providence, RI, 2001. With the cooperation of L. W. Small. MR 1811901, DOI 10.1090/gsm/030
- A. Sankaranarayanan, An identity involving Riemann zeta function, Indian J. Pure Appl. Math. 18 (1987), no. 9, 794–800. MR 908205
- R. Sitaramachandra Rao and B. Davis, Some identities involving the Riemann zeta function. II, Indian J. Pure Appl. Math. 17 (1986), no. 10, 1175–1186. MR 864156
- Wen Peng Zhang, On the several identities of Riemann zeta-function, Chinese Sci. Bull. 36 (1991), no. 22, 1852–1856. MR 1150577
- Wen Peng Zhang, Some identities for Euler numbers, J. Northwest Univ. 22 (1992), no. 1, 17–20 (Chinese, with English summary). MR 1166105
Additional Information
- I-Chiau Huang
- Affiliation: Institute of Mathematics, Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan, Republic of China
- Email: ichuang@math.sinica.edu.tw
- Received by editor(s): November 9, 2010
- Published electronically: April 30, 2012
- Communicated by: Matthew A. Papanikolas
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 2945-2952
- MSC (2010): Primary 11B68; Secondary 16S30
- DOI: https://doi.org/10.1090/S0002-9939-2012-11747-2
- MathSciNet review: 2917068