Zobrazeno 1 - 10
of 161
pro vyhledávání: '"Maier, Helmut"'
Autor:
Maier, Helmut, Rassias, Michael Th.
In previous papers the authors established the prime avoidance property of $k$-th powers of prime numbers and of prime numbers within Beatty sequences. In this paper the authors consider $k$-th powers of Piatetski-Shapiro primes.
Externí odkaz:
http://arxiv.org/abs/2306.16777
Autor:
Maier, Helmut, Rassias, Michael Th.
Let $$\gamma^*:=\frac{8}{9}+\frac{2}{3}\:\frac{\log(10/9)}{\log 10}\:(\approx 0.919\ldots)\:,\ \gamma^*<\frac{1}{c_0}\leq 1\:.$$ Let $\gamma^*<\gamma_0\leq 1$, $c_0=1/\gamma_0$ be fixed. Let also $a_0\in\{0,1,\ldots, 9\}$. In [23] we proved on assump
Externí odkaz:
http://arxiv.org/abs/2108.13132
Autor:
Maier, Helmut, Rassias, Michael Th.
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 various sets of rational numbers in short intervals.
Externí odkaz:
http://arxiv.org/abs/2101.01089
Autor:
Maier, Helmut, Rassias, Michael Th.
Let $$\gamma^*=\frac{8}{9}+\frac{2}{3}\:\frac{\log(10/9)}{\log 10}\:(\approx 0.919\ldots)\:.$$ Let $\gamma^*<\gamma_0\leq 1$, $c_0=1/\gamma_0$ be fixed. Let also $a_0\in\{0,1,\ldots, 9\}$.\\ We prove on assumption of the Generalized Riemann Hypothesi
Externí odkaz:
http://arxiv.org/abs/2006.07873
Autor:
Maier, Helmut, Rassias, Michael Th.
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 various shifts of the argument.
Externí odkaz:
http://arxiv.org/abs/1809.06126
Autor:
Maier, Helmut, Rassias, Michael Th.
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis. These sums contain the M\"obius function and are related to the imaginary part of the Estermann zeta function. The estimate is remarkably sharp in comp
Externí odkaz:
http://arxiv.org/abs/1806.05070
Autor:
Maier, Helmut, Rassias, Michael Th.
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 term in these asymptotic results. In the present paper the authors establ
Externí odkaz:
http://arxiv.org/abs/1806.00772
Autor:
Agarwal, Girish, Allen, Roland, Bezdekova, Iva, Boyd, Robert, Chen, Goong, Hanson, Ronald, Hawthorne, Dean, Hemmer, Philip, Kim, Moochan, Kocharovskaya, Olga, Lee, David, Lidstrom, Sebastian, Lidstrom, Suzy, Losert, Harald, Maier, Helmut, Neuberger, John, Padgett, Miles, Raizen, Mark, Rajendran, Surjeet, Rasel, Ernst, Schleich, Wolfgang, Scully, Marlan, Shchedrin, Gavriil, Shvets, Gennady, Sokolov, Alexei, Svidzinsky, Anatoly, Walsworth, Ronald, Weiss, Rainer, Wilczek, Frank, Willner, Alan, Yablonovich, Eli, Zheludev, Nikolay
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 how the concepts presented at these conferences have transformed scienti
Externí odkaz:
http://arxiv.org/abs/1802.06110
Autor:
Maier, Helmut, Rassias, Michael Th.
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis containing the M\"obius function. The estimate is remarkably sharp in comparison to estimates of other sums containing the M\"obius function. The method
Externí odkaz:
http://arxiv.org/abs/1705.09921