On the Number of Representations of Integers by various Quadratic and Higher Forms

2014/06/02 by Nikos Bagis, Bagis, Nikos, M. L. Glasser +2
Mathematics · #11D45 #11E16 #11E25 #11N37 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications #math.GM #msc:11D45 #msc:11E16 #msc:11E25 #msc:11N37

paper · pdf · doi:10.48550/arxiv.1406.0466

Representation of Integers, Gauss circle problem

openalex publication_date 2014/06/02 · arxiv created 2015/04/29 · arxiv updated 2015/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give formulas for the number of representations of non negative integers by various quadratic forms. We also give evaluations in the case of sum of two cubes (cubic case) and the quintic case, as well. We introduce a class of generalized triangular numbers and give several evaluations. Finally, we present a mean value asymptotic formula for the number of representations of an integer as sum of two squares known as the Gauss circle problem.

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