The polynomial sieve and equal sums of like polynomials

2013/06/28 by Browning, T. D.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1306.6767

Abstract

A new polynomial sieve is presented and used to show that almost all integers have at most one representation as a sum of two values of a given polynomial of degree at least 3.

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• Equal sums of like polynomials
• The larger sieve and polynomial congruences
• On the representation of a polynmial as a sum of mononomials
• Expressing an integer as a sum of cubes of polynomials
• Multiple reciprocal sums and multiple reciprocal star sums of polynomials are almost never integers