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Two random constructions inside lacunary sets

Stefan Neuwirth

Abstract

We study the relationship between the growth rate of an integer sequence and harmonic and functional properties of the corresponding sequence of characters. In particular we show that every polynomial sequence contains a set that is Lamba(p) for all p but is not a Rosenthal set. This holds also for the sequence of primes.

Two random constructions inside lacunary sets

Abstract

We study the relationship between the growth rate of an integer sequence and harmonic and functional properties of the corresponding sequence of characters. In particular we show that every polynomial sequence contains a set that is Lamba(p) for all p but is not a Rosenthal set. This holds also for the sequence of primes.

Paper Structure

This paper contains 8 sections, 13 theorems, 39 equations, 1 table.

Table of Contents

  1. An introduction in French
  2. Position du problème
  3. Constructions aléatoires à l'intérieur de suites lacunaires
  4. Introduction
  5. Equidistributed and Lambda(p) sets
  6. Sets with polynomial growth
  7. Sets that are Lambda(p) for all p
  8. Equidistributed sets

Key Result

Theorem 3.3

There is an equidistributed sequence that is $\Lambda(p)$ for all $p$.

Theorems & Definitions (17)

  • Definition 3.1
  • Theorem 3.3: li98
  • Theorem 3.5: bo88
  • Proposition 3.7: ka73
  • Theorem 3.8
  • Definition 4.1
  • Proposition 4.2
  • Definition 5.1
  • Proposition 5.2
  • Definition 5.3: hk89
  • ...and 7 more