# Combinatorial snapshots

## Related Articles

- All but finitely many non-trivial zeros of the approximations of the Epstein zeta function are simple and on the critical line. Ki, Haseo // Proceedings of the London Mathematical Society;2007, Vol. 94 Issue 2, p543
Some errors, which include Proposition 4.1(2), and typographical mistakes are corrected.

- HYPERGEOMETRIC SERIES ASSOCIATED WITH THE HURWITZ-LERCH ZETA FUNCTION. Bin-Saad, M. G. // Acta Mathematica Universitatis Comenianae;2009, Vol. 78 Issue 2, p269
The present work is a sequel to the papers [3] and [4], and it aims at introducing and investigating a new generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions as particular cases. We study its properties, integral representations,...

- WELL-POISED HYPERGEOMETRIC TRANSFORMATIONS OF EULER-TYPE MULTIPLE INTEGRALS This work was supported by an Alexander von Humboldt research fellowship and partially supported by grant 03-01-00359 of the Russian Foundation for Basic Research.. W. ZUDILIN // Journal of the London Mathematical Society;Aug2004, Vol. 70 Issue 1, p215
Several new multiple-integral representations are proved for well-poised hypergeometric series and integrals. The results yield, in particular, transformations of the multiple integrals that cannot be achieved by evident changes of variable. All this generalizes some classical results of Whipple...

- Zeta functions do not determine class numbers. De Smit, Bart; Perlis, Robert // Bulletin (New Series) of the American Mathematical Society;Oct1994, Vol. 31 Issue 2, p213
Discusses why two number fields sharing the same zeta function do not necessarily have the same class number even if they both have isomorphic adele rings. Theorem and proofs employed.

- Some alternating double sum formulae of multiple zeta values. // Computational & Applied Mathematics;2010, Vol. 29 Issue 3, p375
No abstract available.

- A Note on the Beta Function And Some Properties of Its Partial Derivatives. Nina Shang; Aijuan Li; Zhongfeng Sun; Huizeng Qin // International Journal of Applied Mathematics;2014, Vol. 44 Issue 4, p200
In this paper, the partial derivatives Bp,q(x, y) = âˆ‚q + p/âˆ‚xpâˆ‚yq B(x, y) of the Beta function B(x, y) are expressed in terms of a finite number of the Polygamma function, where p and q are non-negative integers, x and y are complex numbers. In particular, Bp,q(x; y) can be...

- THE BRAUERSIEGEL THEOREM. STPHANE R. LOUBOUTIN // Journal of the London Mathematical Society;Aug2005, Vol. 72 Issue 1, p40
Explicit bounds are given for the residues at $s\,{=}\,1$ of the Dedekind zeta functions of number fields. As a consequence, a simple proof of the Brauer-Siegel theorem and explicit lower bounds for class numbers of number fields are obtained. Compared with Stark's original approach, the paper...

- Summing the Reciprocals of Particular Types of Integers. GRIFFITHS, MARTIN // Mathematical Spectrum;2010/2011, Vol. 43 Issue 3, p98
This article discusses the reciprocals of particular types of integers. It considers the series of reciprocals of the k th powers of square-free integers. It shows how to express S(k) in terms of Riemann zeta functions. In addition, the article demonstrates the series of reciprocals of prime...

- Motivic zeta functions in additive monoidal categories. Kimura, Kenichiro; Kimura, Shun-ichi; Takahashi, Nobuyoshi // Journal of K -- Theory;Jun2012, Vol. 9 Issue 3, p459
Let C be a pseudo-abelian symmetric monoidal category, and X a Schur-finite object of C. We study the problem of rationality of the motivic zeta function Î¶x(t) of X. Since the coefficient ring is not a field, there are several variants of rationality â€” uniform, global, determinantal...