Some consequences of the Riemann hypothesis

DOI10.4064/aa-37-1-339-343zbMath0444.10034OpenAlexW998105725MaRDI QIDQ3887545

Patrick Gallagher

Publication date: 1980

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/205704

zbMATH Keywords

prime number theoremRiemann hypothesisremainder termvon Mangoldt functionSelberg theoremCramer mean value

Mathematics Subject Classification ID

Distribution of primes (11N05)

Related Items (15)

From the Birch and Swinnerton-Dyer conjecture to Nagao’s conjecture ⋮ On Linnik's theorem on Goldbach numbers in short intervals and related problems ⋮ Gallagherian PGT on some compact Riemannian manifolds of negative curvature ⋮ On Koyama's refinement of the prime geodesic theorem ⋮ The prime number theorem for automorphic \(L\)-functions for \(\text{GL}_m\) ⋮ Gallagherian \(PGT\) on \(\mathrm{PSL}(2,\mathbb{Z})\) ⋮ The prime number theorem and pair correlation of zeros of the Riemann zeta-function ⋮ Gallagherian prime geodesic theorem in higher dimensions ⋮ Selberg's integral for Ramanujan automorphic representation ⋮ Selberg's normal density theorem for automorphic \(L\)-functions for \(\mathrm{GL}_m\) ⋮ Prime geodesic theorem for the modular surface ⋮ Estimates of generalized Chebyshev function on \(\mathrm{GL}_m\) ⋮ Computational arithmetic geometry. I: Sentences nearly in the polynomial hierarchy ⋮ On von Koch theorem for \(\mathrm{PSL}(2,\mathbb{Z})\) ⋮ Distribution of Large Gaps Between Primes

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