Abstract
Extending a classical estimate of Mertens for the sum of the reciprocals of the first primes, we provide an explicit remainder formula for products of an arbitrary, but fixed, number of primes.
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References
D. Popa, A double Mertens type evaluation. J. Math. Anal. Appl. 409(2), 1159–1163 (2014)
D. Popa, A triple Mertens evaluation. J. Math. Anal. Appl. 444(1), 464–474 (2016)
G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, vol. 163, Graduate Studies in Mathematics (American Mathematical Society, Providence, 2015)
Acknowledgements
The author wishes to express warm thanks to Dumitru Popa for providing his works on the subject and for subsequent interesting conversations on the problem.
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Tenenbaum, G. (2017). Generalized Mertens Sums. In: Andrews, G., Garvan, F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-68376-8_40
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DOI: https://doi.org/10.1007/978-3-319-68376-8_40
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