On Some Finite Sums with Factorials

Branko Dragovich

On Some Finite Sums with Factorials

数论 2007-05-23 v1 数学物理 math.MP

作者: Branko Dragovich

摘要

The summation formula $\sum^{n-1}_{i=0}\epsilon^i i! (i^k+u_k) = v_k+\epsilon^{n-1} n! A_{k-1}(n)$ $(\epsilon=\pm 1; k=1,2,...; u_k, v_k\in \msbm\hbox{Z}; A_{k-1}$ is a polynomial) is derived and its various aspects are considered. In particular, divisibility with respect to $n$ is investigated. Infinitely many equivalents to Kurepa's hypothesis on the left factorial are found.

关键词

divisor function exponential sums multiplicative functions

引用

@article{arxiv.math/0404487,
  title  = {On Some Finite Sums with Factorials},
  author = {Branko Dragovich},
  journal= {arXiv preprint arXiv:math/0404487},
  year   = {2007}
}

备注

10 pages

On Some Finite Sums with Factorials

摘要

关键词

引用

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