Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral due to Hawkins fully evaluated (analytically continued) produce two infinite series. This new representation, at integer values argument, produces results that consistent with known (values, slope, pole structure). Not surprisingly, studied foun...

In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by second author. Applying Mellin transformation to function, define new class zeta type functions, which is related interpolation functions Apostol–Bernoulli polynomials, Bernoulli Euler polynomials. This Hurwitz alternating Lerch function. Furthermore, using these derive ...

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We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto’s factorization results for biregular bipartite graphs apply, leading to exact factorizations. For (d, r)-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Solé. Finally, we give an example to show how the...

Holomorphic maps between complex manifolds have many properties which distinguish them among general smooth maps. Consider, for example, the case of a map between Riemann surfaces. A holomorphic map is represented locally, in suitable co-ordinates, by one of the models z 7→ z for k ≥ 0. These models are very different from the models of generic smooth maps between surfaces, which are, in additi...

We give a new and bijective proof for the formula of the growth function of the positive braid monoid with respect to Artin generators.

Let f = (f1, . . . , fl) : U → Kl, with K = R or C, be a K-analytic mapping defined on an open set U ⊆ Kn, and let Φ be a smooth function on U with compact support. In this paper, we give a description of the possible poles of the local zeta function attached to (f , Φ) in terms of a log-principalization of the ideal If = (f1, . . . , fl). When f is a non-degenerate mapping, we give an explicit...