A logarithmic estimate for harmonic sums and the digamma function, with an application to the Dirichlet divisor problem

DOI10.1186/S13660-019-2104-9zbMath1499.11374OpenAlexW2947531444MaRDI QIDQ2067893

G. J. O. Jameson

Publication date: 19 January 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-019-2104-9

zbMATH Keywords

divisor problemdigamma functionEuler's constantharmonic sum

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Convergence and divergence of series and sequences (40A05) Gamma, beta and polygamma functions (33B15) Approximation to limiting values (summation of series, etc.) (40A25) Evaluation of number-theoretic constants (11Y60)

Cites Work

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• Estimations of psi function and harmonic numbers
• New sequence converging towards the Euler-Mascheroni constant
• Some quicker classes of sequences convergent to Euler's constant
• Some new convergent sequences and inequalities of Euler's constant
• Sharp bounds for the psi function and harmonic numbers
• A Quicker Convergence to Euler's Constant
• Exponential Sums and Lattice Points III

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