Optimal strong approximation for quadrics over \(\mathbb{F}_q [t]\)

DOI10.1016/j.aim.2022.108852OpenAlexW4313829897MaRDI QIDQ2679897

Masoud Zargar, Naser Talebizadeh Sardari

Publication date: 26 January 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.07839

zbMATH Keywords

function fieldscircle methodRamanujan graphsoptimal strong approximation

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Applications of the Hardy-Littlewood method (11P55) Quadratic forms over global rings and fields (11E12) Varieties over global fields (11G35) Distance in graphs (05C12) Hasse principle, weak and strong approximation, Brauer-Manin obstruction (14G12)

Cites Work

• Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators
• Ramanujan graphs
• Existence and explicit constructions of \(q+1\) regular Ramanujan graphs for every prime power \(q\)
• Ramanujan graphs and exponential sums over function fields
• Optimal strong approximation for quadratic forms
• Rational points on cubic hypersurfaces over \(\mathbb F_q(t)\)
• Diophantine approximation exponents on homogeneous varieties
• A new form of the circle method, and its application to quadratic forms.
• Lifting, restricting and sifting integral points on affine homogeneous varieties
• Diophantine Approximation and Automorphic Spectrum
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