Hurwitz spaces are spaces of pairs S, f where S is a Riemann surface and f : S → ̂ C a meromorphic function. In this work, we study 1-dimensional Hurwitz spaces Hp of meromorphic p-fold functions with four branched points, three of them fixed; the corresponding monodromy representation over each branched point is a product of p − 1 /2 transpositions and the monodromy group is the dihedral group ...

Abstract. The purpose of this paper is to consider a new generalization of the Hurwitz zeta function. Generating functions, Mellin transform, and a series identity are obtained for this generalized class of functions. Some of the results are used to provide a further generalization of the Lambert transform. Relevance with various known results are depicted invariably. Multivariable extensions a...

The properties of the universal Bernoulli polynomials are illustrated and a new class of related L-functions is constructed. A generalization of the Riemann-Hurwitz zeta function is also proposed. Mathematics Subject Classification (2010): 11M41 (primary); 55N22 (secondary).

We study “pure-cycle” Hurwitz spaces, parametrizing covers of the projective line having only one ramified point over each branch point. We start with the case of genus-0 covers, using a combination of limit linear series theory and group theory to show that these spaces are always irreducible. In the case of four branch points, we also compute the associated Hurwitz numbers. Finally, we give a...

This paper studies groups of maximal size acting harmonically on a finite graph. Our main result states that these maximal graph groups are exactly the finite quotients of the modular group Γ = 〈 x, y | x = y = 1 〉 of size at least 6. This characterization may be viewed as a discrete analogue of the description of Hurwitz groups as finite quotients of the (2, 3, 7)-triangle group in the context...

Keywords: Trigonometric functions Hurwitz zeta function Legendre chi function Lerch zeta function Bernoulli polynomials Euler polynomials a b s t r a c t In this sequel to our recent note [D. Cvijović, Values of the derivatives of the cotangent at rational multiples of π, Appl. Math. Lett. it is shown, in a unified manner, by making use of some basic properties of certain special functions, suc...

ABSTRACT In the present paper we evaluate a general integral involving the product of the extension of the Hurwitz-Lerch Zeta function, product of two ,Bessel functions, multivariable Aleph-function Jacobi polynomial, the multivariable I-function defined by Prasad [4] and general class of polynomials of several variables. The importance of the result established in this paper lies in the fact t...

In this paper, we prove that the Hurwitz equivalence problem for 1-factorizations in F2⊕F2 is undecidable, and as a consequence, the Hurwitz equivalence problem for ∆-factorizations in the braid groups Bn, n ≥ 5 is also undecidable.

As is well known, the smallest possible ratio between the spectral norm and the Frobenius norm of an m× n matrix with m ≤ n is 1/ √ m and is (up to scalar scaling) attained only by matrices having pairwise orthonormal rows. In the present paper, the smallest possible ratio between spectral and Frobenius norms of n1×· · ·×nd tensors of order d, also called the best rank-one approximation ratio i...

Patterns for simple continued fractions of the analogues of (xe 2Âf +y)Â(ze 2Âf +w) in the F q [t] case are described. In contrast to the classical case where they consist of arithmetic progressions, in this case they involve an interesting inductive scheme of block repetition and reversals, especially for q=2. 1997 Academic Press This is a sequel to [T2]. For perspective, motivation, and backg...