English

A generalization of the Ross symbols in higher K-groups and hypergeometric functions I

Number Theory 2021-09-14 v3

Abstract

The Ross symbol is defined to be an element {1-z,1-w\} in K_2 of a Fermat curve z^n+w^m=1. Ross showed that it is non-torsion by computing the Beilinson regulator. In this paper, we introduce a generalization of the Ross symbols in K_{d+1} of a variety (1-x_0^{n_0})\cdots(1-x_d^{n_d})=t. The main result is that the Beilinson regulator is described by the hypergeometric functions {}_{d+3}F_{d+2}'s.

Keywords

Cite

@article{arxiv.2003.10652,
  title  = {A generalization of the Ross symbols in higher K-groups and hypergeometric functions I},
  author = {Masanori Asakura},
  journal= {arXiv preprint arXiv:2003.10652},
  year   = {2021}
}

Comments

47 pages, minor revision