English

An extension to the complex plane of the Riemann-Siegel Z function

Classical Analysis and ODEs 2024-11-21 v2

Abstract

The usual Riemann-Siegel Z(t) is a real-valued function. We construct a complex function depending from t and from distance from critical line. It is linked to Riemann Xi(s) function by the same real scaling factor of the usual Riemann-Siegel Z(t) on critical line. Errors are not greater than the errors of Riemann-Siegel Z(t) on the critical line, while this result covers at least the whole critical strip.

Keywords

Cite

@article{arxiv.2107.03191,
  title  = {An extension to the complex plane of the Riemann-Siegel Z function},
  author = {Giovanni Lodone},
  journal= {arXiv preprint arXiv:2107.03191},
  year   = {2024}
}

Comments

42 pages,3 figures