Prime values of \(a^2 + p^4\)

DOI10.1007/s00222-016-0694-0zbMath1405.11124arXiv1504.00531OpenAlexW1691122668MaRDI QIDQ2356920

D. R. Heath-Brown, Xiannan Li

Publication date: 7 June 2017

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

Full work available at URL: https://arxiv.org/abs/1504.00531

zbMATH Keywords

sieveequidistribution of primes

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Applications of sieve methods (11N36) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32)

Related Items

Coordinate distribution of Gaussian primes ⋮ The work of James Maynard ⋮ Variance of the $k$-fold divisor function in arithmetic progressions for individual modulus ⋮ 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 ⋮ Counting primes ⋮ A multiplicative analogue of Schnirelmann's theorem ⋮ On prime values of binary quadratic forms with a thin variable ⋮ Generalized divisor functions in arithmetic progressions: I. ⋮ PRIMES REPRESENTED BY INCOMPLETE NORM FORMS ⋮ Prime values of a sparse polynomial sequence ⋮ Rational points and prime values of polynomials in moderately many variables ⋮ A cubic analogue of the Friedlander-Iwaniec spin over primes

Cites Work

• The polynomial \(X^2+Y^4\) captures its primes
• Asymptotic sieve for primes
• Gaussian sequences in arithmetic progressions
• Gaussian primes
• On the representation of primes by cubic polynomials in two variables
• Primes represented by \(x^3+ 2y^3\)
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