A Tauberian theorem with remainder for the Laplace transform and its application in the theory of the Riemann zeta-function

DOI10.1007/BF01061813zbMath0786.11056OpenAlexW2062594108MaRDI QIDQ1181628

V. I. Mel'nik

Publication date: 27 June 1992

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01061813

zbMATH Keywords

Laplace transformRiemann zeta-functionasymptotic formulaTauberian theoremerror termDirichlet divisor problem

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) (zeta (s)) and (L(s, chi)) (11M06) Laplace transform (44A10) Tauberian theorems (40E05) Tauberian theorems (11M45)

Cites Work

• Some new estimates in the Dirichlet divisor problem
• Applications of Tauberian theorems with remainder for the Laplace transform in probability theory
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