A conditional density theorem for the zeros of the Riemann zeta-function
A conditional result on Goldbach numbers in short intervals
A Large Sieve Density Estimate near ?= 1.
A Lower Bound for the de Bruijn-Newman Constant ... .
A mean value estimate for real character sums
A new Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant .
A new lower bound for the de Bruijn-Newman constant.
A note on the zeros of the derivative of the Riemann zeta function near the critical line
A numerical bound for small prime solutions of some ternary linear equations
A Proof of the Prime Number Summation Formula Without Assuming the Riemann Hypothesis.
A Proof of the Prime Number Summation Formula Without Assuming the Riemann Hypothesis. (Short Communication).
A sequential Riesz-like criterion for the Riemann Hypothesis.
A singular series average and Goldbach numbers in short intervals
A strategy for proving Riemann hypothesis.
A strengthening of the Nyman-Beurling criterion for the Riemann hypothesis
According to the well-known Nyman-Beurling criterion the Riemann hypothesis is equivalent to the possibility of approximating the characteristic function of the interval in mean square norm by linear combinations of the dilations of the fractional parts for real greater than . It was conjectured and established here that the statement remains true if the dilations are restricted to those where the ’s are positive integers. A constructive sequence of such approximations is given.
A zero density result for the Riemann zeta function
We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.
Abundant numbers and the Riemann hypothesis.
An Alternative Form of the Functional Equation for Riemann’s Zeta Function, II
This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for . We present here, after showing the first proof of Riemann, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta function and the alternating Zeta function, connected with odd numbers. A proof that Euler himself could have arranged with a little step at the end of his paper “Remarques sur un beau rapport entre...
An Asymptotic Formula for a sum Involving Zeros of the Riemann Zeta-function
An identity for sums of polylogarithm functions.