Related papers: A congruence with the Euler totient function
This article aims to find explicit congruences between Dirichlet characters and gives various results on how to find some effectively on a computer. It ends with concrete examples putting those ideas in application.
In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain…
In this paper we propose a construction of $p$-adic Euler $\ell$-function using Kubota-Leopoldt's approach and Washington's one. We also compute the derivative of $p$-adic Euler $\ell$-function at $s=0$ and the values of $p$-adic Euler…
In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.
In this paper our aim is to deduce some sharp Tur\'an type inequalities for the remainder $q-$exponential functions. Our results are shown to be a generalization of results which were obtained by Alzer \cite{al}.
A detailed analysis of the remainder obtained by truncating the Euler series up to the $n$th-order term is presented. In particular, by using an approach recently proposed by Weniger, asymptotic expansions of the remainder, both in inverse…
In this work, a mode of convergence for measurable functions is introduced. A related notion of Cauchy sequence is given and it is proved that this notion of convergence is complete in the sense that Cauchy sequences converge. Moreover, the…
In this note we give a characterization of taut Riemannian foliations using the transverse divergence. This result turns out to be a convenient tool in the case of some standard examples. Furthermore, we show that a classical tautness…
In this paper, we present experimental algorithms for solving the dualization problem. We present the results of extensive experimentation comparing the execution time of various algorithms.
In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to…
We present some Euler-type recurrences for the partition function $p(n)$.
In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geometric polynomials, Bernoulli and Euler numbers.
Let $\phi(n)$ be the Euler totient function and $\phi_k(n)$ its $k$-fold iterate. In this note, we improve the upper bound for the number of positive $n\leqslant x$ such that $\phi_{k+1}(n)\geqslant cn$. Comparing with the upper bound which…
We survey some results on toric topology.
We give a functional equation for the refined Herglotz-Zagier function. It is analogous to a result in the theory of modular forms.
We first survey the known results on functional equations for the double zeta-function of Euler type and its various generalizations. Then we prove two new functional equations for double series of Euler-Hurwitz-Barnes type with complex…
We review some results of calculations, having the property of maximal transcendentality.
We prove certain conjecture holds true for a finite category which has M\"obius inversion. The conjecture states a relationship between the zeta function of a finite category and the Euler characteristic of a finite category.
This paper has two parts. The first part surveys Euler's work on the constant gamma=0.57721... bearing his name, together with some of his related work on the gamma function, values of the zeta function and divergent series. The second part…
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.