The polynomials X2+(Y2+1)2$X^2+(Y^2+1)^2$ and X2+(Y3+Z3)2$X^{2} + (Y^3+Z^3)^2$ also capture their primes

DOI10.1112/plms.12557arXiv2112.03617OpenAlexW4386001853MaRDI QIDQ6185888

Jori Merikoski

Publication date: 9 January 2024

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.03617

zbMATH Keywords

prime numberHarman's sieve methodcorrelations of hyper-Kloosterman sumssparse polynomial set

Mathematics Subject Classification ID

Applications of sieve methods (11N36) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• New equidistribution estimates of Zhang type
• 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
• The polynomial \(X^2+Y^4\) captures its primes
• Asymptotic sieve for primes
• Prime values of a sparse polynomial sequence
• Prime values of \(a^2 + p^4\)
• Exponential sums over definable subsets of finite fields
• A general stratification theorem for exponential sums, and applications
• Primes Represented by Binary Cubic Forms
• The largest prime factor of the integers in an interval, II
• Gaussian primes
• Primes from sums of two squares and missing digits
• PRIMES REPRESENTED BY INCOMPLETE NORM FORMS
• On Exponential Sums in Finite Fields
• On Some Exponential Sums
• Primes represented by \(x^3+ 2y^3\)

This page was built for publication: The polynomials X2+(Y2+1)2$X^2+(Y^2+1)^2$ and X2+(Y3+Z3)2$X^{2} + (Y^3+Z^3)^2$ also capture their primes