Related papers: A Function in the Congruence Theory

We give a constructive, metastable formulation of a theorem about the exchange of limits for convergent sequence $L^1$ functions. A crucial tool is a one-dimensional version of Szemeredi's regularity lemma for $L^1$ functions.

This work introduces the class of generalized linear-quadratic functions, constructed using maximally monotone symmetric linear relations. Calculus rules and properties of the Moreau envelope for this class of functions are developed. In…

A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…

Extending the work of Freese, we further develop the theory of generalized trigonometric functions. In particular, we study to what extent the notion of polar form for the complex numbers may be generalized to arbitrary associative…

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…

We evaluate certain multidimensional integrals in terms of the Lerch transcendent function $\Phi$, generalizing Guillera-Sondow's formulas. As an application, we get new representations of classical constants like Euler's constant $\gamma$…

Here presented is a unified approach to Stirling numbers and their generalizations as well as generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, and generalized divided difference. Previous…

The current work revisits the results of L.F. Meyers and R. See in [3], and presents the census-taker problem as a motivation to introduce the beautiful theory of numbers.

In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.

A classical theorem of Menshov states that every measurable function can redefined on a set of arbitrarily small Lebesgue measure, so that the resulting function has uniformly convergent Fourier series. We prove that the same is true if we…

Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through…

Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen's generalized polylogarithms.

We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute…

In the present paper, we give a brief review of $L^{1}$-convergence of trigonometric series. Previous known results in this direction are improved and generalized by establishing a new condition.

We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…

The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been…

The conception of C- and H-representations of any holomorphic function is further extended to the notions, definitions, lemmas and theorems of the complex integration. On this basis and the introduced notion of a H-plane, generalising the…

Let P -> M be a principal G-bundle. Using techniques from the loop representation of gauge theory, we construct well-defined substitutes for ``Lebesgue measure'' on the space A of connections on P and for ``Haar measure'' on the group Ga of…

Generalized trigonometric functions with two parameters were introduced by Dr\'{a}bek and Man\'{a}sevich to study an inhomogeneous eigenvalue problem of the $p$-Laplacian. Concerning these functions, no multiple-angle formula has been known…

In this article we give a result obtained of an experimental way for the Euler totient function.