Pairs of Diagonal Quartic Forms: The Asymptotic Formulae

DOI10.1093/IMRN/RNAD021arXiv2211.10397OpenAlexW4327944102WikidataQ130442416 ScholiaQ130442416MaRDI QIDQ6142306

Jörg Brüdern, Trevor D. Wooley

Publication date: 25 January 2024

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: We establish an asymptotic formula for the number of integral solutions of bounded height for pairs of diagonal quartic equations in $26$ or more variables. In certain cases, pairs in $25$ variables can be handled.

Full work available at URL: https://arxiv.org/abs/2211.10397

zbMATH Keywords

asymptotic formulaediagonal quartic forms

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Counting solutions of Diophantine equations (11D45) Diophantine equations in many variables (11D72) Hasse principle, weak and strong approximation, Brauer-Manin obstruction (14G12)

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