Publications (18)
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…
The ternary Goldbach problem with a prime with a missing digit and primes of special types
Helmut Maier, Michael Th. Rassias
Let $$γ^*:=\frac{8}{9}+\frac{2}{3}\:\frac{\log(10/9)}{\log 10}\:(\approx 0.919\ldots)\:,\ γ^*<\frac{1}{c_0}\leq 1\:.$$ Let $γ^*<γ_0\leq 1$, be fixed. Let also $a_0…
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…
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…
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…