Related papers: The $\theta=\infty$ conjecture implies the Riemann…
The Riemann Hypothesis can be reformulated as statements about the eigenvalues of certain matrices whose entries are defined in terms of the Taylor coefficients of the zeta function. These eigenvalues exhibit interesting visual patterns…
In this paper we show that the $\theta$ invariant generalizes the Rozansky-Overbay invariant.
In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by…
The goal of this paper is twofold; on one hand we wish to present some statements that can be formulated in terms of Interpolation theory which are equivalent to the truth or the falseness of the Riemann Hypothesis, on the other hand we…
We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute…
We investigate the screw line corresponding to the screw function associated with the Riemann zeta-function under the Riemann hypothesis and derive three necessary and sufficient conditions for the Riemann hypothesis as applications. One of…
Approximation in measure is employed to solve an asymptotic Dirichlet problem on arbitrary open sets and to show that many functions, including the Riemann zeta-function, are universal in measure. Connections with the Riemann Hypothesis are…
The Riemann Hypothesis (RH), one of the most profound unsolved problems in mathematics, concerns the nontrivial zeros of the Riemann zeta function. Establishing connections between the RH and physical phenomena could offer new perspectives…
L. de Branges proposed an approach to the Riemann hypothesis using certain positivity conditions. In this paper, the authors examine this approach and indicate its difficulty.
In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.
One of equivalents of the Riemann hypothesis is Li's criterion that all Li coefficients are positive. We study recurrence relations of Li coefficients in this note.
In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…
Let $\pi S(t)$ denote the argument of the Riemann zeta-function at the point $\frac12+it$. Assuming the Riemann Hypothesis, we sharpen the constant in the best currently known bounds for $S(t)$ and for the change of $S(t)$ in intervals. We…
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
Some identities for the Riemann zeta-function are proved, using properties of the Mellin transform and M\"untz's identity.
We present an infinite family of Borwein type $+ - - $ conjectures. The expressions in the conjecture are related to multiple basic hypergeometric series with Macdonald polynomial argument.
A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.
Two identities extracted from the literature are coupled to obtain an integral equation for Riemann's $\xi(s)$ function, and thus $\zeta(s)$ indirectly. The equation has a number of simple properties from which useful derivations flow, the…