Prime Twins and Siegel Zeros

DOI10.1112/plms/s3-47.2.193zbMath0517.10044OpenAlexW2081183524MaRDI QIDQ3665205

D. R. Heath-Brown

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1112/plms/s3-47.2.193

zbMATH Keywords

Deuring-Heilbronn phenomenonsieve methodsL-functionsbounds for Kloosterman sumsexistence of infinitely many prime twinsexistence of Siegel zeros

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gauss and Kloosterman sums; generalizations (11L05) Applications of sieve methods (11N36) Distribution of primes (11N05)

Related Items (24)

Goldbach's problem ⋮ Zeros of Rankin-Selberg \(L\)-functions at the edge of the critical strip ⋮ The Temptation of the Exceptional Characters ⋮ Sign changes of Kloosterman sums and exceptional characters ⋮ On the Hardy–Littlewood–Chowla conjecture on average ⋮ Exceptional zeros, sieve parity, Goldbach ⋮ Primes in tuples. II ⋮ On multiplicative functions on consecutive integers ⋮ Enveloping sieve related to the Hardy-Littlewood irreducible tuple conjecture in a function field ⋮ Prime tuples and Siegel zeros ⋮ The prime-pair conjectures of Hardy and Littlewood ⋮ Bilinear forms in Weyl sums for modular square roots and applications ⋮ Representation of integers by a family of cubic forms ⋮ A note on Dirichlet \(L\)-functions ⋮ The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures ⋮ Exceptional characters and nonvanishing of Dirichlet \(L\)-functions ⋮ On the convolution of the Liouville function under the existence of Siegel zeros ⋮ Twin primes via exceptional characters ⋮ Landau's problems on primes ⋮ Uniform bounds for the least almost‐prime primitive root ⋮ Some remarks on Landau-Siegel zeros ⋮ On smooth gaps between consecutive prime numbers ⋮ Levels of distribution and the affine sieve ⋮ Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim

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