Asymptotic expansions of the prime counting function

DOI10.1016/j.jnt.2021.07.032OpenAlexW3202954316WikidataQ113870344 ScholiaQ113870344MaRDI QIDQ2162797

Jesse Elliott

Publication date: 9 August 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.06633

zbMATH Keywords

Stieltjes transformexponential integrallogarithmic integralasymptotic expansionprime number theoremcontinued fractionnumber fieldarithmetic semigroupprime counting function

Mathematics Subject Classification ID

Asymptotic results on counting functions for algebraic and topological structures (11N45) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Zeta functions and (L)-functions of number fields (11R42) Continued fractions; complex-analytic aspects (30B70) Distribution of primes (11N05) Generalized primes and integers (11N80)

Cites Work

• The Hilbert transform of a measure
• The operad Lie is free
• Continued fractions with applications
• A note on Mertens' formula for arithmetic progressions
• A general prime number theorem
• Inversion of series and the cohomology of the moduli spaces $\mathcal{M}^{\delta}_{0,n}$
• Subgroups of Finite Index in Free Groups
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