The main purpose of this paper is to present new q-extensions of Apostol’s type Euler polynomials using the fermionic p-adic integral on Zp. We define the q-λ-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define qextensions of Apostol type’s Euler polynomials of higher order using the multivariate fermionic p-adic integral ...

Riesz potentials also called Riesz fractional derivatives and their Hilbert transforms are computed for the Korteweg-de Vries soliton. They are expressed in terms of the full-range Hurwitz Zeta functions ζ s, a and ζ− s, a . It is proved that these Riesz potentials and their Hilbert transforms are linearly independent solutions of a Sturm-Liouville problem. Various new properties are establishe...

We prove a simultaneous generalization of the classical Riemann-Hurwitz and Plücker formulas, addressing total number inflection points morphism from (smooth, projective) curve to an arbitrary higher-dimensional variety. Our definition point is relative algebraic family divisors on target variety, our formula obtained using theory localized top Chern classes. In assigning multiplicities points,...

We proved that the Hurwitz zeta function is prime. In addition, we derived Nevanlinna characteristic for this function.

For a given group G the orientably regular maps with orientation-preserving automorphism are used as vertices of graph O(G), undirected and directed edges showing effect duality hole operations on these maps. Some examples graphs given, including several for small Hurwitz groups. some G, such affine groups AGL1(2e), O(G) is connected, whereas other infinite families, alternating symmetric group...

In this note, Kharitonov's theorem on robust Hunvitz poljmomials is simplified for low-order polynomials. Specifically, for n = 3, 4, and 5, the number of polynomials required to check robust stability is one, two, and three, respectively, instead of four. Furthermore, it is shown that for n > 6, the number of polynomials for robust stability checking is necessarily four, thus further simplific...

Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...