A paucity problem associated with a shifted integer analogue of the divisor function

2021/07/31 by Winston Heap, Heap, Winston, Anurag Sahay +3
Mathematics · #11D45 #11N37 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2108.00287

openalex publication_date 2021/07/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Suppose that θ is irrational. Then almost all elements ν∈ \mathbb Z[θ] that may be written as a k-fold product of the shifted integers n+θ (n∈ \mathbb N) are thus represented essentially uniquely.

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