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pro vyhledávání: '"11M26"'
Autor:
Gonek, Steven M., Sahay, Anurag
Let $0<\gamma_1\leq \gamma_2 \leq \cdots $ denote the ordinates of nontrivial zeros of the Riemann zeta function with positive imaginary parts. For $c>0$ fixed (but possibly small), $T$ large, and $\gamma_n\leq T$, we call a gap $\gamma_{n+1}-\gamma_
Externí odkaz:
http://arxiv.org/abs/2412.15481
Autor:
Bellotti, Chiara, Wong, Peng-Jie
In this article, we improve the recent work of Hasanalizade, Shen, and Wong by establishing $$\left| N (T) - \frac{T}{ 2 \pi} \log \left( \frac{T}{2\pi e}\right) \right|\le 0.10076\log T+0.24460\log\log T+8.08292$$ for every $T\ge e$, where $N(T)$ is
Externí odkaz:
http://arxiv.org/abs/2412.15470
Autor:
Lodone, Giovanni
We try to apply a known equivalence, for RH about Riemann Z function, to Dirichlet L functions with primitive characters. The aim is to give a small contribution to the proof of the generalized version of Riemann Hypothesis (RH).
Comment: 21 pag
Comment: 21 pag
Externí odkaz:
http://arxiv.org/abs/2412.00169
Assuming the Generalized Riemann Hypothesis and a pair correlation conjecture for the zeros of Dirichlet $L$-functions, we establish the truth of a conjecture of Montgomery (in its corrected form stated by Friedlander and Granville) on the magnitude
Externí odkaz:
http://arxiv.org/abs/2411.19762
Autor:
Akatsuka, Hirotaka
Ramanujan investigated maximal order for the number of divisors function by introducing some notion such as (superior) highly composite numbers. He also studied maximal order for other arithmetic functions including the sum of powers of divisors func
Externí odkaz:
http://arxiv.org/abs/2411.19259
Autor:
Zhao, Tianyu
For $i\in \{1,2,3\}$, let $E_i(x)$ denote the error term in each of the three theorems of Mertens on the asymptotic distribution of prime numbers. We show that for each $i\in \{1,2\}$, the Riemann hypothesis is equivalent to the condition $\int_2^X E
Externí odkaz:
http://arxiv.org/abs/2411.18903
Autor:
Rezvyakova, I. S.
It is proved that the Epstein zeta-function corresponding to a binary positive definite quadratic form with integer coefficients has a positive proportion of its non-trivial zeros on the critical line.
Comment: 75 pages
Comment: 75 pages
Externí odkaz:
http://arxiv.org/abs/2411.18492
Autor:
Maw, Aung Phone
We demonstrate the general outlines of a method for obtaining analytic expressions for certain types of general arithmetical sums. In particular, analytical expressions for a general arithmetical sum whose terms are summed over either the positive in
Externí odkaz:
http://arxiv.org/abs/2411.17327
Autor:
Johnston, Daniel R.
We demonstrate the impact of a generic zero-free region and zero-density estimate on the error term in the prime number theorem. Consequently, we are able to improve upon previous work of Pintz and provide an essentially optimal error term for some c
Externí odkaz:
http://arxiv.org/abs/2411.13791
Autor:
Hang, Peng-Cheng, Luo, Min-Jie
For any $a\in\mathbb{C}$, the zeros of $\zeta(s)-a$, denoted by $\rho_a=\beta_a+i\gamma_a$, are called $a$-points of the Riemann zeta function $\zeta(s)$. In this paper, we reformulate some basic results about the $a$-points of $\zeta(s)$ shown by Ga
Externí odkaz:
http://arxiv.org/abs/2411.13255