The ideal counting function in cubic fields

2015/03/04 by Zhishan Yang, Yang, Zhishan
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1503.01318

arxiv created 2015/03/04 · openalex publication_date 2015/03/04 · arxiv updated 2015/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a cubic algebraic extension K of ℚ, the behavior of the ideal counting function is considered in this paper. Let a_K(n) be the number of integral ideals of the field K with norm n. An asymptotic formula is given for the sum ∑_n₁²+n₂²≤ xa_K(n₁²+n₂²).

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