Pairs of diagonal quartic forms: the asymptotic formulae
Joerg Bruedern, Trevor D. Wooley
TL;DR
This paper develops asymptotic formulas to estimate the number of integral solutions within bounded height for pairs of diagonal quartic equations in at least 26 variables, extending to some cases with 25 variables.
Contribution
It provides new asymptotic formulas for counting solutions to pairs of diagonal quartic forms in higher dimensions, advancing understanding in this area.
Findings
Established asymptotic formulas for 26+ variables
Extended results to some cases with 25 variables
Improved understanding of solutions to diagonal quartic equations
Abstract
We establish an asymptotic formula for the number of integral solutions of bounded height for pairs of diagonal quartic equations in or more variables. In certain cases, pairs in variables can be handled.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems