We give a number field analogue of result Ramanujan, Hardy and Littlewood, thereby obtaining modular relation involving the non-trivial zeros Dedekind zeta function. also provide Riesz-type criterion for Generalized Riemann Hypothesis ζK(s). New elegant transformations are obtained when K is quadratic extension, one which involves modified Bessel function second kind.

Abstract Motivated by the recent studies and developments of integral transforms with various special matrix functions, including orthogonal polynomials as kernels, in this article we derive formulas for Fourier cosine sine functions involving generalized Bessel polynomials. With help these several results are obtained, which extensions corresponding standard cases. The given here general chara...

This paper consists of three parts. In part I, we microscopically derive Ginzburg– Landau (GL) theory from BCS theory for translation-invariant systems in which multiple types of superconductivity may coexist. Our motivation are unconventional superconductors. We allow the ground state of the effective gap operator KTc + V to be n-fold degenerate and the resulting GL theory then couples n order...

We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well established strategy to deal with scaling critical perturbations of dispersive PDEs, we make use Hankel transform rely on some precise Bessel functions. As complementary result, local smoothing estimate the Klein-Gordon equation same field.

There is a rich literature on the study of Bessel and Riesz potentials on the Euclidean space R, see for example the books [23, 20, 1, 16] and the references therein. However, little is known on how to extend the Bessel and Riesz potentials to metric measure spaces in a reasonable way. This issue is interesting in that it is closely related with the study of various current topics, such as the ...

Let aIp(x) = ∑ n 0 (x/2)2n+p n!Γ(p + an + 1) be the Galué’s generalized modified Bessel function depending on parameters a = 0, 1, 2, . . . and p > −1. Consider the function aI p : R → R, defined by aI p(x) = 2pΓ(p+1)x−paIp(x). Motivated by the inequality of Lazarević, namely cosh x < ( sinh x x )3 for x = 0, in order to generalize this inequality we prove that the Turán-type, Lazarević-type in...

• In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet processes. • To a GGC variable, one may associate a unique Thorin measure. Let G a positive r.v. and Γt(G) ( resp. Γt(1/G) ) the Generalized Gamma Convolution with Thorin measure t-times the law of G (resp. ...

Special functions such as hypergeometric, zeta, Bessel, Whittaker, Struve, Airy, Weber-Hermite and Mittag-Leffler are obtained a solution to complex differential equations in engineering, science technology. In this work, generalized Euler-type integrals involving four parameters function proposed. Some special cases of type that corresponding well-known results the literature also inferred.