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Partial Liouville sums over divisors

Milo Moses

Abstract

Using sieves and elementary manipulations, we show that the signs of partial sums of the Liouville function over divisors are in a strong sense equally distributed.

Partial Liouville sums over divisors

Abstract

Using sieves and elementary manipulations, we show that the signs of partial sums of the Liouville function over divisors are in a strong sense equally distributed.
Paper Structure (3 sections, 4 theorems, 18 equations)

This paper contains 3 sections, 4 theorems, 18 equations.

Table of Contents

  1. Introduction
  2. Details and proof
  3. Acknowledgements

Key Result

Theorem 1.1

Let $(a_{n,x})_{n\geq 1}$ be a sequence of complex numbers depending on $x$ such that If the limits exist for all $z$, then they tend to $0$ as $z$ tends to infinity.

Theorems & Definitions (8)

  • Theorem 1.1
  • Proposition 1
  • proof
  • Lemma 2.1
  • proof
  • Corollary 2.1
  • proof
  • proof : Proof of Theorem \ref{['THEOREM']}