Yochay Jerby

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20172025

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math.GM2024

The $A$ -philosophy for the Hardy $Z$ -Function

Yochay Jerby

In recent works we have introduced the parameter space $Z_{N}$ of $A$ -variations of the Hardy $Z$ -function, $Z (t)$ , whose elements are functions of the form \begin{equation…

math.GM2024

On Edwards' Speculation and a New Variational Method for the Zeros of the $Z$ -Function

Yochay Jerby

In his foundational book, Edwards introduced a unique "speculation" regarding the possible theoretical origins of the Riemann Hypothesis, based on the properties of the Riemann-Sie…

math.GM2024

On the approximation of the Hardy $Z$ -function via high-order sections

Yochay Jerby

Sections of the Hardy $Z$ -function are given by $Z_{N} (t) := \sum_{k = 1}^{N} \frac{cos ( θ ( t ) - l n ( k ) t )}{k}$ for any $N \in N$ . Sections approximate the Hardy $Z$ -functi…

math.GM2017

An experimental study of the monotonicity property of the Riemann zeta function

Yochay Jerby

In 1970, based on newly available empiric evidence, a remarkable monotonicity property for $∣ ζ (z) ∣$ was conjectured by R. Spira. The $ζ$ -monotonicity property can be written as f…

math.GM2017

On Fermat curves modulo a finite number

Yochay Jerby

We show that the existence of a non-trivial solution of $x^{n} + y^{n} = p^{n}$ , with $p$ a prime number, is equivalent to the existence of a solution of a certain (over-determined) system o…

The A-philosophy for the Hardy Z-Function

On Edwards' Speculation and a New Variational Method for the Zeros of the Z-Function

On the approximation of the Hardy Z-function via high-order sections

An experimental study of the monotonicity property of the Riemann zeta function

On Fermat curves modulo a finite number

The $A$ -philosophy for the Hardy $Z$ -Function

On Edwards' Speculation and a New Variational Method for the Zeros of the $Z$ -Function

On the approximation of the Hardy $Z$ -function via high-order sections