The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces

Brandes, Julia; Parsell, Scott T.

doi:10.2140/ant.2021.15.2289

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1944-7833 (e-only)

ISSN: 1937-0652 (print)

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces

Julia Brandes and Scott T. Parsell

Vol. 15 (2021), No. 9, 2289–2314

DOI: 10.2140/ant.2021.15.2289

Abstract

We establish the analytic Hasse principle for Diophantine systems consisting of one diagonal form of degree $k$ and one general form of degree $d$ , where $d$ is smaller than $k$ . By employing a hybrid method that combines ideas from the study of general forms with techniques adapted to the diagonal case, we are able to obtain bounds that grow exponentially in $d$ but only quadratically in $k$ , reflecting the growth rates typically obtained for both problems separately. We also discuss some of the most interesting generalisations of our approach.

PDF Access Denied

We have not been able to recognize your IP address 18.218.25.67 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

Hardy–Littlewood method, diagonal forms, forms in many variables

Mathematical Subject Classification

Primary: 11D72

Secondary: 11D45, 11P55, 14G05

Milestones

Received: 18 May 2020

Revised: 19 December 2020

Accepted: 23 February 2021

Published: 23 December 2021

Authors

Julia Brandes
University of Gothenburg and Chalmers University of Technology Gothenburg Sweden

Scott T. Parsell
West Chester University West Chester, PA United States

Vol. 15, No. 9, 2021