Translator Disclaimer
March 2017 Small solutions of diagonal congruences
Todd Cochrane, Misty Ostergaard, Craig Spencer
Funct. Approx. Comment. Math. 56(1): 39-48 (March 2017). DOI: 10.7169/facm/1587

Abstract

We prove that for $k \geq 2$, $0 <\varepsilon< \frac 1{k(k-1)}$, $n>\frac {k-1}{\varepsilon }$, prime $p> P(\varepsilon, k)$, and integers $c,a_i$, with $p \nmid a_i$, $1 \le i \le n$, there exists a solution $\underline{x}$ to the congruence $$ \sum_{i=1}^n a_ix_i^k \equiv c \mod p $$ in any cube $\mathcal{B}$ of side length $b \ge p^{\frac 1k + \varepsilon}$. Various refinements are given for smaller $n$ and for cubes centered at the origin.

Citation

Download Citation

Todd Cochrane. Misty Ostergaard. Craig Spencer. "Small solutions of diagonal congruences." Funct. Approx. Comment. Math. 56 (1) 39 - 48, March 2017. https://doi.org/10.7169/facm/1587

Information

Published: March 2017
First available in Project Euclid: 27 January 2017

zbMATH: 06864144
MathSciNet: MR3629009
Digital Object Identifier: 10.7169/facm/1587

Subjects:
Primary: 11D72, 11D79
Secondary: 11L03

Rights: Copyright © 2017 Adam Mickiewicz University

JOURNAL ARTICLE
10 PAGES

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

SHARE
Vol.56 • No. 1 • March 2017
Back to Top