Squares: Additive questions and partitions

Robert C. Vaughan

doi:10.1142/S1793042115400096

Squares: Additive questions and partitions

Robert C. Vaughan

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

This memoir is concerned with a number of additive questions in which squares occur. For ternary additive problems with at least one square, the exceptional set is considered and it is shown that current methods cannot be sharpened substantially. In a different direction, but using cognate methods, an asymptotic formula is obtained for the number of partitions of a number into squares.

Original language	English (US)
Pages (from-to)	1367-1409
Number of pages	43
Journal	International Journal of Number Theory
Volume	11
Issue number	5
DOIs	https://doi.org/10.1142/S1793042115400096
State	Published - Aug 5 2015

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1142/S1793042115400096

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title = "Squares: Additive questions and partitions",

abstract = "This memoir is concerned with a number of additive questions in which squares occur. For ternary additive problems with at least one square, the exceptional set is considered and it is shown that current methods cannot be sharpened substantially. In a different direction, but using cognate methods, an asymptotic formula is obtained for the number of partitions of a number into squares.",

author = "Vaughan, {Robert C.}",

note = "Funding Information: The research was supported in part by NSA Grant Number H98230-12-1-0276. Publisher Copyright: {\textcopyright} 2015 World Scientific Publishing Company.",

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AB - This memoir is concerned with a number of additive questions in which squares occur. For ternary additive problems with at least one square, the exceptional set is considered and it is shown that current methods cannot be sharpened substantially. In a different direction, but using cognate methods, an asymptotic formula is obtained for the number of partitions of a number into squares.

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Squares: Additive questions and partitions

Abstract

All Science Journal Classification (ASJC) codes

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