Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár

In their paper from 2012, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this paper, we answer positively the integral homology version of their question in the case of abelian varieties, and the rational homology version in the case of compact ball quotients. We also propose several conjectures in relation to the Singer–Hopf conjecture in the complex projective setting.

Next-to-leading-logarithm threshold resummation for exclusive B meson decays

We extend the threshold resummation of the large logarithms $$\ln x$$ ln x which appear in factorization formulas for exclusive B meson decays, x being a spectator momentum fraction, to the next-to-leading-logarithm (NLL) accuracy. It is shown that the NLL resummation effect provides suppression in the end-point region with $$x\sim 0$$ x ∼ 0 stronger than the leading-logarithm (LL) one, and thus improves perturbative analyses of the above processes. We revisit the $$B\rightarrow K\pi $$ B → K π decays under the NLL resummation in the perturbative QCD approach, and find that it induces up to 20% variation of the direct CP asymmetries in various modes relative to the LL results. Our method to avoid the Landau singularity in the inverse Mellin transformation causes at most 10% theoretical uncertainty.

A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function

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

Some Properties for Multiple Twisted (p, q)-L-Function and Carlitz’s Type Higher-Order Twisted (p, q)-Euler Polynomials

The main goal of this paper is to study some interesting identities for the multiple twisted ( p , q ) -L-function in a complex field. First, we construct new generating functions of the new Carlitz-type higher order twisted ( p , q ) -Euler numbers and polynomials. By applying the Mellin transformation to these generating functions, we obtain integral representations of the multiple twisted ( p , q ) -Euler zeta function and multiple twisted ( p , q ) -L-function, which interpolate the Carlitz-type higher order twisted ( p , q ) -Euler numbers and Carlitz-type higher order twisted ( p , q ) -Euler polynomials at non-positive integers, respectively. Second, we get some explicit formulas and properties, which are related to Carlitz-type higher order twisted ( p , q ) -Euler numbers and polynomials. Third, we give some new symmetric identities for the multiple twisted ( p , q ) -L-function. Furthermore, we also obtain symmetric identities for Carlitz-type higher order twisted ( p , q ) -Euler numbers and polynomials by using the symmetric property for the multiple twisted ( p , q ) -L-function.

Some Properties of Extended Hypergeometric Function and Its Transformations

There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended Gauss hypergeometric function in one, two and more variables.

A (p,v)-Extension of Hurwitz-Lerch Zeta Function and its Properties

In this paper, we define a (p,v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81–106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results.