An algebraic approach to count the number of representations of an integer by the quadratic form x²+ay² for certain values of a

2022/08/04 by Thanathat Dechakulkamjorn, Dechakulkamjorn, Thanathat, Nithi Rungtanapirom +1
Mathematics · #11D09 #11D45 #11D72 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2208.02454

openalex publication_date 2022/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By considering the norm of elements in the ring of integers in ℚ(√(-a)), we give an algebraic approach to count the number of integral solutions of diophantine equations of the form x²+ay²=n where a is a Heegner number or a=27.

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