Related papers: A generalization of Carlitz's congruence
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
Explicit formulas involving a generalized Ramanujan sum are derived. An analogue of the prime number theorem is obtained and equivalences of the Riemann hypothesis are shown. Finally, explicit formulas of Bartz are generalized.
Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…
Several terminating generalizations of Ramanujan's formula for $\frac{1}{\pi}$ with complete WZ proofs are given.
We present inequalities and some applications to Kellers' limit and Carlemans' inequality.
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
Girstmair in [1, Theorem 1] gave a generalization of Murty's irreducibility criterion (see [2, Theorem 1]). In this article, we further generalize these criteria.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
A new generalization of the classical separate algebraicity theorem is suggested and proved.
We devote this paper to provide an abstract generalization of an iteration originally due to K\"all\'en, and revisited later by Kr\"oner, that might be of independent interest.
In this paper, we generalized the classical Fermat point, proved the sufficient and necessary condition for uniqueness and existence for the generalized Fermat point(GFP) theorem, and discuss some interesting geometric property of the…
This is an elementary explanation of a cubic composition formula due to Ramanujan.
In this paper, we investigate the extent to which the Bump-Hoffstein conjecture could be generalized for central coverings of general linear groups. We provide evidence for such generalized Bump-Hoffstein conjecture by proving some special…
We present a generalization of a formula of higher order derivatives and give a short proof.
In this paper, we consider the Carlitz's type q-analogue of Changhee numbers and polynomials and we give some explicit formulae for these numbers and polynomials.
This paper evaluates some generalised Euler sums involving the digamma function.
We prove a generalized Fej\'er's theorem for locally compact groups.