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Zeros of the dilogarithm


Author: Cormac O’Sullivan
Journal: Math. Comp. 85 (2016), 2967-2993
MSC (2010): Primary 33B30, 30C15; Secondary 11P82
Published electronically: March 2, 2016
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Abstract: We show that the dilogarithm has at most one zero on each branch, that each zero is close to a root of unity, and that they may be found to any precision with Newton's method. This work is motivated by applications to the asymptotics of coefficients in partial fraction decompositions considered by Rademacher. We also survey what is known about zeros of polylogarithms in general.


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Additional Information

Cormac O’Sullivan
Affiliation: Department of Mathematics, The CUNY Graduate Center, New York, New York 10016-4309
Email: cosullivan@gc.cuny.edu

DOI: https://doi.org/10.1090/mcom/3065
Keywords: Dilogarithm zeros, Newton's method, polylogarithms
Received by editor(s): February 19, 2015
Published electronically: March 2, 2016
Additional Notes: Support for this project was provided by a PSC-CUNY Award, jointly funded by The Professional Staff Congress and The City University of New York.
Article copyright: © Copyright 2016 American Mathematical Society