## 61 Citations

### Almost all of the nontrivial zeros of the Riemann zeta-function are on the critical line

- Mathematics, Philosophy
- 2022

Applying Littlewood’s lemma in connection to Riemann’s Hypothesis and exploiting the symmetry of Riemann’s xi function we show that almost all nontrivial Riemann’s Zeta zeros are on the critical line.

### On the Epstein zeta function and the zeros of a class of Dirichlet series

- Mathematics
- 2021

By generalizing the classical Selberg-Chowla formula, we establish the analytic continuation and functional equation for a large class of Epstein zeta functions. This continuation is studied in order…

### Explicit zero density estimate for the Riemann zeta-function near the critical line

- Mathematics
- 2019

. In 1946, A. Selberg proved N ( σ, T ) ≪ T 1 − 14 ( σ − 12 ) log T where N ( σ,T ) is the number of nontrivial zeros ρ of the Riemann zeta-function with ℜ{ ρ } > σ and 0 < ℑ{ ρ } ≤ T . We provide an…

### On the Riemann Hypothesis for the Zeta Function

- Mathematics
- 2021

In this paper we address some variants for the products of Hadamard and Patterson. We prove that all zeros of the Riemann $\Xi$--function are real. We also prove that the Riemann hypothesis is true.…

### All Complex Zeros of the Riemann Zeta Function Are on the Critical Line: Two Proofs of the Riemann Hypothesis

- MathematicsSSRN Electronic Journal
- 2020

I present two independent proofs of the Riemann Hypothesis considered by many the greatest unsolved problem in mathematics. I find that the admissible domain of complex zeroes of the Riemann Zeta…

### Critical zeros of lacunary $L$-functions

- MathematicsActa Arithmetica
- 2020

Assuming the existence of a sequence of exceptional discriminants of quadratic fields, we show that a hundred percent of zeros of the Riemann zeta function are on the critical line in specific…

### An Analytical and Numerical Detour for the Riemann Hypothesis

- MathematicsInf.
- 2021

From the functional equation of Riemann's zeta function, new insight is given into Hadamard's product formula and the method can be extended to other meromorphic functions, in the neighborhood of isolated zeros, inspired by the Weierstraß canonical form.

### DISTRIBUTION OF THE ZEROS OF LINEAR COMBINATIONS OF L (cid:0) DIRICHLET FUNCTIONS LYING ON THE CRITICAL LINE

- Mathematics
- 2015

Some problems of the number theory are associated with the zeros of special functions, such as the Riemann zeta function (cid:16) ( s ) , Dirichlet L-functions L ( s; (cid:31) ) and others. The…

### Mean value theorems for the Apostol-Vu double zeta-function and its application

- Mathematics
- 2022

. Mean value theorems for various double zeta-functions have been studied. In this paper, we consider mean square values of the Apostol-Vu type. In addition, we also obtain mean square value of the…

### The rightness of the Riemann hypothesis

- Mathematics
- 2016

The finite covering theorem and symmetry properties of several functions are utilized to show that if $0<a<1$, all zeros of the zeta function are on the line $Re(z)=\frac{1}{2}$.

## References

SHOWING 1-10 OF 26 REFERENCES

### Critical zeros of the Riemann zeta-function

- Mathematics
- 2014

In this unpublished note, we sketch an idea of using a three-piece mollifier to slightly improve the known percentages of zeros and simple zeros of the Riemann zeta-function on the critical line.…

### The Theory of the Riemann Zeta-Function

- Mathematics
- 1987

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects…

### Long mollifiers of the Riemann Zeta-function

- Mathematics
- 1993

The best current bounds for the proportion of zeros of ζ( s ) on the critical line are due to Conrey [C], using Levinson's method [Lev]. This method can also be used to detect simple zeros on the…

### More than two fifths of the zeros of the Riemann zeta function are on the critical line.

- Mathematics
- 1989

In this paper we show that at least 2/5 of the zeros of the Riemann zeta-function are simple and on the critical line. Our method is a refinement of the method Levinson [11] used when he showed that…

### Zeros of the Riemann zeta function on the critical line

- Mathematics, Philosophy
- 2010

### The Riemann Zeta-Function and Hecke Congruence Subgroups. II

- Mathematics
- 2007

This is a rework of our old file, which has been left unpublished since September 1994, on an explicit spectral decomposition of the fourth power moment of the Riemann zeta-function against a weight…

### More than 41% of the zeros of the zeta function are on the critical line

- Mathematics, Philosophy
- 2011

We prove that at least 41.05% of the zeros of the Riemann zeta function are on the critical line.

### Applications of the L‐functions ratios conjectures

- Mathematics
- 2005

In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios of products of shifted L‐functions. In this paper we will present various…

### The twisted fourth moment of the Riemann zeta function

- Mathematics
- 2007

Abstract We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length .