Rational points on complete intersections over \mathbbF_q(t)

2019/07/16 by Pankaj Vishe, Vishe, Pankaj
Computer Science · Mathematics · #11G35 #11P55 #11T55 #14G05 #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1907.07097

openalex publication_date 2019/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Kloosterman refinement for function fields K=\mathbbF_q(t) is developed and used to establish the quantitative arithmetic of the set of rational points on a smooth complete intersection of two quadrics X⊂ ℙ^n-1_K , under the assumption that q is odd and n≥ 9.

Citations

• Representations of integers by systems of three quadratic forms

Related

• Rationality of complete intersections of two quadrics
• Explicit Estimates for the Number of Rational Points of Singular Complete Intersections over a Finite Field
• Rational points on singular intersections of quadrics
• Rationality of even-dimensional intersections of two real quadrics
• Number of rational points of symmetric complete intersections over a finite field and applications