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Jacob's ladders and the equivalent of the Fermat-Wiles theorem generated by the Hardy-Littlewood formula (1921)

Jan Moser

Abstract

In this paper we prove that the 105 years old Lemma 18 of Hardy and Littlewood from theirs fundamental paper \cite{2} is able to generate, for example, a continuum set of new $ζ$-equivalents of the Fermat-Wiles theorem.

Jacob's ladders and the equivalent of the Fermat-Wiles theorem generated by the Hardy-Littlewood formula (1921)

Abstract

In this paper we prove that the 105 years old Lemma 18 of Hardy and Littlewood from theirs fundamental paper \cite{2} is able to generate, for example, a continuum set of new -equivalents of the Fermat-Wiles theorem.
Paper Structure (4 sections, 63 equations)

This paper contains 4 sections, 63 equations.

Table of Contents

  1. Introduction
  2. Jacob's ladders: notions and basic geometrical properties
  3. New $\zeta$-functional and corresponding $\zeta$-equivalent of the Fermat-Wiles theorem generated by the Hardy-Littlewood Lemma 18
  4. Remarks on A. A. Karatsuba's use of my results on eq. $Z'(t)=0$ in his paper dedicated to the 90th. anniversary of I. M. Vinogradov

Theorems & Definitions (20)

  • remark 1
  • remark 2
  • remark 3
  • remark 4
  • remark 5
  • remark 6
  • remark 7
  • remark 8
  • remark 9
  • remark 12
  • ...and 10 more