7 citations · 10 across the 16 of their papers we have counts for
18 papers
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\{…
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…
Cotangent sums related to the Riemann Hypothesis for various shifts of the argument
Helmut Maier, Michael Th. Rassias
One of the approaches to the Riemann Hypothesis is the Nyman-Beurling criterion. Cotangent sums play a significant role. Here we investigate the values of these cotangent sums for…
Explicit estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis. These sums contain the Möbius function and are related to the imaginary part of t…
The error for the second moment of cotangent sums related to the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
In various papers the authors have derived asymptotics for moments of certain cotangent sums related to the Riemann Hypothesis. S. Bettin has given an upper bound for the error ter…
Light, the universe, and everything -- 12 Herculean tasks for quantum cowboys and black diamond skiers
Girish Agarwal, Roland Allen, Iva Bezdekova +29
The Winter Colloquium on the Physics of Quantum Electronics (PQE) has been a seminal force in quantum optics and related areas since 1971. It is rather mindboggling to recognize ho…
Estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis containing the Möbius function. The estimate is remarkably sharp in comparison to…
A criterion related to the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
A crucial role in the Nyman-Beurling-Báez-Duarte approach to the Riemann Hypothesis is played by the distance \[ d_N^2:=\inf_{A_N}\frac{1}{2π}\int_{-\infty}^\infty\left|1-ζA_N\left…
Asymptotics for moments of certain cotangent sums for arbitrary exponents
Helmut Maier, Michael Th. Rassias
In this paper we extend a result on the asymptotics of moments of certain cotangent sums associated to the Estermann and Riemann zeta functions established in a previous paper for…
Asymptotics for moments of certain cotangent sums
Helmut Maier, Michael Th. Rassias
In this paper we improve a result on the order of magnitude of certain cotangent sums associated to the Estermann and the Riemann zeta functions.
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…
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…