Generalized Sato-Tate and quadratic residues

2025/09/08 by Sergey Vladuts, Vladuts, Sergey
Mathematics · #11A15 #11G05 #11G20 #14G15 #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2509.07183

openalex publication_date 2025/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Generalized Sato-Tate Conjecture permits to obtain rather precise information on the distribution of the consecutive quadratic residues modulo large primes.

Citations

• On the Sato-Tate conjecture for non-generic abelian surfaces

Related

• Consecutive Quadratic Residues And Quadratic Nonresidue Modulo p
• A refinement of Sato-Tate conjecture
• On consecutive quadratic non-residues: a conjecture of Issai Schur
• Distribution of modular inverses and multiples of small integers and the Sato--Tate conjecture on average
• Nonuniform Distributions of Residues of Prime Sequences in Prime Moduli