## 112 Citations

On the Speiser equivalent for the Riemann hypothesis

- Mathematics
- 2015

Speiser showed that the Riemann hypothesis is equivalent to the absence of non-trivial zeros of the derivative of the Riemann zeta-function left of the critical line. We investigate the relationship…

Zeros of higher derivatives of Riemann zeta function

- Mathematics
- 2021

Abstract. In this article, we refined the error term of some results of Levinson and Montgomery [22], Ki and Lee [20] on zero density estimates of ζ. We also have shown that all most all zeros of…

An Argument in Confirmation of the Riemann Hypothesis.

- Mathematics
- 2018

Based on results due to Taylor, Lagarias and Suzuki, and Ki, the relationship between the zeros of two combinations of the Riemann zeta function and the function itself is considered. A…

Arguments Related to the Riemann Hypothesis: New Methods and Results

- Philosophy, Mathematics
- 2018

Four propositions are considered concerning the relationship between the zeros of two combinations of the Riemann zeta function and the function itself. The ﬁrst is the Riemann hypothesis, while the…

The completed zeta function and the Riemann Hypothesis

- Mathematics
- 2014

The famous Riemann Hypothesis asserts that all the non-trivial zeros of the zeta function have real part 1 . Based on some recent computer calculations showing that the first discovered 10 trillion…

On the distribution of the zeros of the derivative of the Riemann zeta-function

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2014

Abstract We establish an asymptotic formula describing the horizontal distribution of the zeros of the derivative of the Riemann zeta-function. For ℜ(s) = σ satisfying (log T)−1/3+ε ⩽ (2σ − 1) ⩽ (log…

ANOTHER PROOF OF SPIRA'S INEQUALITY AND ITS APPLICATION TO THE RIEMANN HYPOTHESIS

- Mathematics
- 2013

By using new inequalities involving powers of rational functions, we give another proof of an important Spira's relation for the Riemann zeta-function |ζ(1 −s)| |ζ(s)| in the strip 0 < ℜs < 1/2, |ℑs|…

On the exact location of the non-trivial zeros of Riemann's zeta function

- Mathematics
- 2013

In this paper we introduce the real valued real analytic function kappa(t) implicitly defined by exp(2 pi i kappa(t)) = -exp(-2 i theta(t)) * (zeta'(1/2-it)/zeta'(1/2+it)) and kappa(0)=-1/2. (where…

Results Connected to the Riemann Hypothesis

- Mathematics
- 2012

In his famous presentation at the International Congress of Mathematicians held in Paris in 1900, David Hilbert included the Riemann Hypothesis (all the non-trivial zeros of the zeta function have…