Tangent power sums and their applications

Vladimir Shevelev; Peter J. C. Moses

Tangent power sums and their applications

Number Theory 2014-08-01 v6

Authors: Vladimir Shevelev , Peter J. C. Moses

Abstract

For integer $m, p,$ we study tangent power sum $\sum^m_{k=1}\tan^{2p}\frac{\pi k}{2m+1}.$ We prove that, for every $m, p,$ it is integer, and, for a fixed p, it is a polynomial in $m$ of degree $2p.$ We give recurrent, asymptotical and explicit formulas for these polynomials and indicate their connections with Newman's digit sums in base $2m.$

Keywords

divisor function exponential sums pi computation

Cite

@article{arxiv.1207.0404,
  title  = {Tangent power sums and their applications},
  author = {Vladimir Shevelev and Peter J. C. Moses},
  journal= {arXiv preprint arXiv:1207.0404},
  year   = {2014}
}

Comments

14 pages. Addition of reference: A.M. and I.M. Yaglom (1953)

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