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Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918) and their relation to the Titchmarsh's sums (1943) and the Fermat-Wiles theorem

Jan Moser

Abstract

In this paper we give some new consequences that follow from our formula for increments of the Hardy-Littlewood integral. The main of these ones are $\mathcal{T}_1$ and $\mathcal{T}_2$ equivalents of the Fermat-Wiles theorem.

Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918) and their relation to the Titchmarsh's sums (1943) and the Fermat-Wiles theorem

Abstract

In this paper we give some new consequences that follow from our formula for increments of the Hardy-Littlewood integral. The main of these ones are and equivalents of the Fermat-Wiles theorem.
Paper Structure (5 sections, 73 equations)

This paper contains 5 sections, 73 equations.

Table of Contents

  1. Introduction
  2. Jacob's ladders and proliferation of every $L_2$-orthogonal system
  3. Variant of the first Titchmarsh's formula
  4. Connection between increments of the Hardy-Littlewood integral and increments of the first Titchmarsh's function $\mathcal{T}_1(x)$
  5. $\mathcal{T}_1$ and $\mathcal{T}_2$ equivalents of the Fermat-Wiles theorem

Theorems & Definitions (5)

  • remark 1
  • remark 2
  • remark 3
  • remark 4
  • remark 5