Möbius cancellation on polynomial sequences and the quadratic Bateman-Horn conjecture over function fields

DOI10.1007/s00222-022-01115-yzbMath1503.11077arXiv2008.09905OpenAlexW3081117837WikidataQ123237893 ScholiaQ123237893MaRDI QIDQ2152487

Mark Shusterman, William F. Sawin

Publication date: 8 July 2022

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.09905

zbMATH Keywords

Möbius functionglobal function fieldsétale cohomologyDirichlet characterstrace functionsChowla conjectureparity barrierquadratic Bateman-Horn conjectureshort character sums

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Asymptotic results on arithmetic functions (11N37) Goldbach-type theorems; other additive questions involving primes (11P32) Étale and other Grothendieck topologies and (co)homologies (14F20) Quadratic forms over global rings and fields (11E12) Varieties over global fields (11G35) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Estimates on character sums (11L40) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Global ground fields in algebraic geometry (14G25) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32)

Related Items

On the Chowla and twin primes conjectures over \(\mathbb{F}_q[T\)], The tamely ramified geometric quantitative minimal ramification problem, Bilinear forms with Kloosterman and Gauss sums in function fields

Cites Work

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• Average bounds for Kloosterman sums over primes
• Square-full polynomials in short intervals and in arithmetic progressions
• Singularities and vanishing cycles in number theory over function fields
• On character sums of binary quadratic forms
• Transformation de Fourier et majoration de sommes exponentielles. (Fourier transformation and majoration of exponential sums.)
• Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier
• Seminaire de géométrie algébrique du Bois-Marie 1965-66 SGA 5 dirige par A. Grothendieck avec la collaboration de I. Bucur, C. Houzel, L. Illusie, J.-P. Jouanolou et J. -P. Serre. Cohomologie \(\ell\)-adique et fonctions L
• The polynomial \(X^2+Y^4\) captures its primes
• Nonresonance conditions for arrangements.
• On short sums of trace functions
• On the conductor of cohomological transforms
• Fourier uniformity of bounded multiplicative functions in short intervals on average
• Nearby cycles of parahoric shtukas, and a fundamental lemma for base change
• Algebraic twists of modular forms and Hecke orbits
• The fourth moment of quadratic Dirichlet \(L\)-functions over function fields
• Discriminants, resultants, and multidimensional determinants
• Algebraic trace functions over the primes
• Seminar of algebraic geometry du Bois-Marie 1963--1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 1: Topos theory. Exp. I--IV
• On the number of divisors of quadratic polynomials
• Higher order Fourier analysis of multiplicative functions and applications
• Shifted convolution and the Titchmarsh divisor problem over 𝔽_q[t]
• Sums of Values of Nonprincipal Characters over Shifted Primes
• Lectures on applied ℓ-adic cohomology
• Prime specialization in genus 0
• Traces of high powers of the Frobenius class in the hyperelliptic ensemble
• The Distribution of Galois Groups and Hilbert's Irreducibility Theorem
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• Sur certaines sommes d'exponentielles sur les nombres premiers
• On the representation of primes by cubic polynomials in two variables
• Fonctions arithmétiques et formes binaires irréductibles de degré 3
• Monodromy of Hyperplane Sections of Curves and Decomposition Statistics over Finite Fields
• TENSOR AND CONVOLUTION DIRECT IMAGE OF ℓ‐ADIC SHEAVES
• Introductory course on $\ell$-adic sheaves and their ramification theory on curves
• Galois Groups and Fundamental Groups
• PRIMES REPRESENTED BY INCOMPLETE NORM FORMS
• Plus grand facteur premier de valeurs de polynômes aux entiers
• On the Bateman–Horn conjecture for polynomials over large finite fields
• THE PARITY PROBLEM FOR REDUCIBLE CUBIC FORMS
• The expression of a polynomial as a sum of three irreducibles
• On Dirichlet Characters of Polynomials
• Almost-primes represented by quadratic polynomials
• Almost-primes represented by quadratic polynomials