Translator Disclaimer
2018 Minimal Degrees of Genocchi-Peano Functions: Calculus Motivated Number Theoretical Estimates
Krzysztof Chris Ciesielski
Real Anal. Exchange 43(2): 281-292 (2018). DOI: 10.14321/realanalexch.43.2.0281

Abstract

A rational function of the form \(\frac{x_1^{\alpha_1} x_2^{\alpha_2} \cdots x_n^{\alpha_n}}{x_1^{\beta_1} + x_2^{\beta_2}+\cdots + x_n^{\beta_n}}\) is a Genocchi-Peano example, GPE, provided it is discontinuous, but its restriction to any hyperplane is continuous. We show that the minimal degree \(D(n)\) of a GPE of \(n\)-variables equals \(2\left\lfloor \frac{e^2}{e^2-1} n \right\rfloor+2i\) for some \(i\in\{0,1,2\}\). We also investigate the minimal degree \(D_b(n)\) of a bounded GPE of \(n\)-variables and note that \(D(n)\leq D_b(n)\leq n(n+1)\). Finding better bounds for the numbers \(D_b(n)\) remains an open problem.

Citation

Download Citation

Krzysztof Chris Ciesielski. "Minimal Degrees of Genocchi-Peano Functions: Calculus Motivated Number Theoretical Estimates." Real Anal. Exchange 43 (2) 281 - 292, 2018. https://doi.org/10.14321/realanalexch.43.2.0281

Information

Published: 2018
First available in Project Euclid: 27 June 2018

zbMATH: 06924889
MathSciNet: MR3942578
Digital Object Identifier: 10.14321/realanalexch.43.2.0281

Subjects:
Primary: 11A25
Secondary: 26B05

Rights: Copyright © 2018 Michigan State University Press

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.43 • No. 2 • 2018
Back to Top