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Jacob's ladders, Hardy-Littlewood integral (1918) and new asymptotic functional equations for Euler's Gamma function together with the tenth equivalent of the Fermat-Wiles theorem

Jan Moser

Abstract

In this paper new $Γ$-functional is constructed upon the basis of the set of almost linear increments of the Hardy-Littlewood integral. This functional generates a $Γ$-equivalent of the Fermat-Wiles theorem and also new set of factorization formulae for Euler's $Γ$-function.

Jacob's ladders, Hardy-Littlewood integral (1918) and new asymptotic functional equations for Euler's Gamma function together with the tenth equivalent of the Fermat-Wiles theorem

Abstract

In this paper new -functional is constructed upon the basis of the set of almost linear increments of the Hardy-Littlewood integral. This functional generates a -equivalent of the Fermat-Wiles theorem and also new set of factorization formulae for Euler's -function.
Paper Structure (7 sections, 105 equations)

This paper contains 7 sections, 105 equations.

Table of Contents

  1. Introduction
  2. List of equivalents of the Fermat-Wiles theorem
  3. The first lemma as the asymptotic Newton-Leibniz formula for the function $|\zeta\left(\frac{1}{2}+it\right)|^2$
  4. Next lemmas and therorem 1
  5. New factorization formulas for the Euler's Gamma-function
  6. Further formulas
  7. On a localized $\zeta$-equivalent of the Fermat-Wiles theorem

Theorems & Definitions (13)

  • remark 1
  • remark 2
  • remark 3
  • remark 4
  • remark 5
  • remark 6
  • remark 7
  • remark 8
  • remark 9
  • remark 10
  • ...and 3 more