We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the ...

Our goal in this article is to use ideas from symmetric q-calculus operator theory the study of meromorphic functions on punctured unit disc and propose a novel q-difference for these functions. A few additional classes are then defined light new operator. We prove many useful conclusions regarding newly constructed functions, such as convolution, subordination features, integral representation...

where I is a finite set of distinct tuples (α0,α1, . . . ,αk) for which eachαi is a nonnegative integer, and the aᾱ are meromorphic functions in D = {z | |z| < 1}. For some index sets I, we determine conditions on aᾱ, whereby a meromorphic solution f of (1.1) in D will have finite order of growth as measured by the Ahlfors-Shimizu characteristic function. In [1], Bank investigated (1.1) where I...

A rigid meromorphic cocycle is a class in the first cohomology of the discrete group Γ := SL2(Z[1/p]) with values in the multiplicative group of non-zero rigid meromorphic functions on the p-adic upper half planeHp := P1(Cp)−P1(Qp). Such a class can be evaluated at the real quadratic irrationalities in Hp, which are referred to as “RM points”. The RM values of arbitrary rigid meromorphic cocycl...

Rigid meromorphic cocycles were introduced by Darmon and Vonk as a conjectural p-adic extension of the theory singular moduli to real quadratic base fields. They are certain cohomology classes \({{\,\mathrm{SL}\,}}_2(\mathbb {Z}[1/p])\) which can be evaluated at irrationalities, values thus obtained conjectured lie in algebraic extensions field. In this article, we present construction inspired...

The generalized Stirling numbers introduced recently [11, 12] are considered in detail for the particular case s = 2 corresponding to the meromorphic Weyl algebra. A combinatorial interpretation in terms of perfect matchings is given for these meromorphic Stirling numbers and the connection to Bessel functions is discussed. Furthermore, two related q-polynomial identities are derived.

Let f : X → X be a dominant meromorphic map on a projective manifold X which preserves a meromorphic fibration π : X → Y of X over a projective manifold Y. We establish formulas relating the dynamical degrees of f , the dynamical degrees of f relative to the fibration and the dynamical degrees of the map g : Y → Y induced by f. Applications are given.

Let μ̃ be a partially Artinian graph. Is it possible to compute anti-n-dimensional groups? We show that there exists a left-dependent, meromorphic, arithmetic and sub-additive factor. A central problem in classical discrete K-theory is the construction of ideals. Recently, there has been much interest in the computation of meromorphic groups.

‎We consider the uniqueness problem of algebroid functions‎ ‎on an angular domain‎. ‎Several theorems are established to extend the uniqueness theory of meromorphic functions to algebroid functions‎.

In this paper we prove a theorem demonstrating the characterization property associated with certain families of functions, which are multivalently analytic and multivalently meromorphic (for particular values of q) in the open unit domain E. Some consequences of the main result are also mentioned.