The Riemann Conjecture and the advanced Calculus Methods for Physics

TL;DR

This paper offers new proofs in advanced calculus related to conformal mappings and explores a novel approach to the Riemann conjecture by linking it to the positivity of a specific numerical series.

Contribution

It provides detailed proofs of conformal mapping formulas and introduces a new perspective on the Riemann conjecture connecting it to numerical series positivity.

Findings

New proof of Cissoti integral formula

Reduction of Riemann conjecture to series positivity

Mathematical physics perspective on the Riemann conjecture

Abstract

We present a set of lectures on topics of advanced calculus in one real and complex variable with several new results and proofs on the subject, specially with detailed proof-always missing in the literature - of the Cissoti explicitly integral formula conformally representing a polygon onto a disc.Besides we present-in the paper appendix-a new study embodied with a mathematical physicist perspective,on the famous Riemann conjecture on the zeros of the Zeta function, reducing its proof to a conjecture on the positivity of a numerical series.