Counting S₅-fields with a power saving error term

2013/10/08 by Arul Shankar, Jacob Tsimerman, Shankar, Arul +1 · 1 citation
Mathematics · #11R45 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1310.1998

openalex publication_date 2013/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how the Selberg Λ²-sieve can be used to obtain power saving error terms in a wide class of counting problems which are tackled using geometry of numbers. Specifically, we give such an error term for the counting function of S₅-quintic fields.

Citations

• Most hyperelliptic curves over Q have no rational points
• Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves

Cited by

• Counting C₂ \wr S₄ fields with a power saving error term

Related

• An error estimate for counting S₃-sextic number fields
• Counting multi-quadratic number fields of bounded discriminant
• Twins of s-free numbers
• Power Savings for Counting (Twisted) Abelian Extensions of Number Fields
• Secondary terms in the counting functions of quartic fields II