Related papers: Generalization of Romanoff's theorem

Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the…

We prove the following generalisation of Bohr theorem : let $K\subset\mathbb C$ a continuum, $(F_n)_n$ its Faber polynomials, $\Omega_R=\{\Phi_K<R\}, (R>1)$ the levels sets of the Green function; then there exists $R_0>1$ such that for any…

We generalize Pappus chain theorem and give an analogue to this theorem.

We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.

We prove a simple formula for the main value of $r$-even functions and give applications of it. Considering the generalized Ramanujan sums $c_A(n,r)$ involving regular systems $A$ of divisors we show that it is not possible to develop a…

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schr\"odinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking…

Many papers have been published over the years that either conjecture or even (claim to) prove the universality of the form of Maxwell's equations. We present yet another derivation of Maxwell's equations and discuss the conclusions…

Generic Newton polygons for L-functions of exponential sums associated to Laurent polynomials in one variable are determined. The corresponding Hasse polynomials are also determined.

We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

We generalize Deligne's approach to tame geometric class field theory to the case of a relative curve, with arbitrary ramification.

We prove a formula for the Taylor series coefficients of a zero of the sum of a complex-exponent polynomial and a base function which is a general holomorphic function with a simple zero. Such a Taylor series is more general than a Puiseux…

The goal of this article is to give a positive answer to Rockafellar's maximality of the sum conjecture in the linear multi-valued operator case.

From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…

In this paper we propose generalizations of the Sokolov-Ternov and Unruh effects, and discuss the possibility to measure them on different experiments.

We begin with recalling the correspond theorem of induced modules and global sections of vector bundles. After that, we give a generalization of this theorem. Finally, we apply the result to branching laws, and give some concrete examples.

We provide numerical procedures for possibly best evaluating the sum of positive series. Our procedures are based on the application of a generalized version of Kummer's test.

We resolve a conjecture of Rystov concerning products of matrices, that generalizes the \v{C}ern\'y Conjecture.

In this paper we find the partial sums of two kinds normalized Wright functions and the partial sums of Alexander transform of these normalized Wright functions.

We prove a short general theorem which immediately implies some classical results of Hasse, Guillera and Sondow, Paolo Amore, and also Alzer and Richards. At the end we obtain a new representation for the Euler constant gamma. The theorem…