Non trivial zeros of the Zeta function using the differential equations

Walid OUKIL

doi:10.33774/coe-2023-sb63n-v4

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Non trivial zeros of the Zeta function using the differential equations

23 January 2024, Version 4

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Working Paper

Walid OUKIL

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Abstract

We investigate a relationship between differential equations and the Zeta function. We obtain a more flexible representation of the Riemann Zeta function in the critical strip. This allows us to prove that the Zeta function does not vanish at any point $s\in\mathbb{C}$ such that $\Re(s)\in (0,2^{-1})$.

Keywords

Zeta function

Differential equations

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