1 citations · 6 across the 29 of their papers we have counts for
16 papers · 1 filter
The behaviour of a certain additive function in large intervals between consecutive primes
Michael Th. Rassias
We investigate the behaviour of a certain additive function depending on prime divisors of specific integers lying in large gaps between consecutive primes. The result is obtained…
Recent results on large gaps between primes
Michael Th. Rassias
One of the themes of this paper is recent results on large gaps between primes. The first of these results has been achieved in the paper [12] by Ford, Green, Konyagin and Tao. It…
Prime Avoidance Property of -th Powers of Piatetski-Shapiro Primes
Helmut Maier, Michael Th. Rassias
In previous papers the authors established the prime avoidance property of -th powers of prime numbers and of prime numbers within Beatty sequences. In this paper the authors co…
The ternary Goldbach problem with a prime with a missing digit and primes of special types
Helmut Maier, Michael Th. Rassias
Let Let , be fixed. Let also $a_0\in\{…
Double exponential lower bounds for possible solutions in the Second Case of the Fermat Last Theorem
Preda Mihăilescu, Michael T. Rassias
In a recent paper, the first author provided some lower bounds to solutions of the equations of Fermat and Catalan, based on local power series developments at the ramified prime o…
On the maximum of cotangent sums related to the Riemann Hypothesis in rational numbers in short intervals
Helmut Maier, Michael Th. Rassias
Cotangent sums play a significant role in the Nyman-Beurling criterion for the Riemann Hypothesis. Here we investigate the maximum of the values of these cotangent sums over variou…
The ternary Goldbach problem with two Piatetski-Shapiro primes and a prime with a missing digit
Helmut Maier, Michael Th. Rassias
Let Let , be fixed. Let also .\\ We prove…
The ternary Goldbach problem with a prime and two isolated primes
Helmut Maier, Michael Th. Rassias
In the present paper we prove that under the assumption of the GRH (Generalized Riemann Hypothesis) each sufficiently large odd integer can be expressed as the sum of a prime and t…
Trigonometric representations of generalized Dedekind and Hardy sums via the discrete Fourier transform
Michael Th. Rassias, László Tóth
We introduce some new higher dimensional generalizations of the Dedekind sums associated with the Bernoulli functions and of those Hardy sums which are defined by the sawtooth func…
Large gaps between consecutive prime numbers containing perfect -th powers of prime numbers
Helmut Maier, Michael Th. Rassias
Let be a fixed natural number. We establish the existence of infinitely many pairs of consecutive primes , satisfying $$ p_{n+1}-p_n\geq c\:\frac{\log p_n\…
Large gaps between consecutive prime numbers containing square-free numbers and perfect powers of prime numbers
Helmut Maier, Michael Th. Rassias
We prove a modification as well as an improvement of a result of K. Ford, D. R. Heath-Brown and S. Konyagin concerning prime avoidance of square-free numbers and perfect powers of…
The order of magnitude for moments for certain cotangent sums
Helmut Maier, Michael Th. Rassias
We settle a question on the rate of growth of the moments of cotangent sums considered by the authors in their previous papers [8], [9]. We even obtain the true order of magnitude…
The rate of growth of moments of certain cotangent sums
Helmut Maier, Michael Th. Rassias
We consider cotangent sums associated to the zeros of the Estermann zeta function considered by the authors in their previous paper [5]. We settle a question on the rate of growth…
Generalizations of a cotangent sum associated to the Estermann zeta function
Helmut Maier, Michael Th. Rassias
Cotangent sums are associated to the zeros of the Estermann zeta function. They have also proven to be of importance in the Nyman-Beurling criterion for the Riemann Hypothesis. The…
A Multidimensional Hilbert-Type Integral Inequality Related to the Riemann Zeta Function
Michael Th. Rassias, Bicheng Yang
In this paper,using methods of weight functions and techniques of real analysis, we provide a multidimensional Hilbert-type integral inequality with a homogeneous kernel of degree…
On the representation of the number of integral points of an elliptic curve modulo a prime number
Michael Th. Rassias
In this paper we shall investigate the problem of the representation of the number of integral points of an elliptic curve modulo a prime number p. We present a way of expressing a…