Algebraic structures of Euler numbers

Huang, I-Chiau

doi:10.1090/S0002-9939-2012-11747-2

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