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A note on an asymptotic expansion related to the Dickman function

  • C. S. Franze
Article

Abstract

In this paper we refine an asymptotic expansion given by Soundararajan (Ramanujan J 29(1–3):25–30 2012) for a family of multiple integrals related to the Dickman function. The result suggests a relatively simple approach to computing these integrals numerically.

Keywords

Dickman function Linear sieve Polylogarithms 

Mathematics Subject Classification

11N25 11N99 

Notes

Acknowledgements

I would like to thank the American Institute of Mathematics for providing me the opportunity to participate in the workshop on Bounded gaps between primes, and fostering the lively intellectual atmosphere that inspired this manuscript.

References

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    Franze, C.S.: A family of multiple integrals connected with relatives of the Dickman function. J. Number Theory 179, 33–49 (2017)MathSciNetCrossRefGoogle Scholar
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    Soundararajan, K.: An asymptotic expansion related to the Dickman function. Ramanujan J. 29(1–3), 25–30 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA

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