Abstract
We establish the analytic Hasse principle for Diophantine systems consisting of one diagonal form of degree and one general form of degree , where is smaller than . 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 but only quadratically in , reflecting the growth rates typically obtained for both problems separately. We also discuss some of the most interesting generalisations of our approach.
Citation
Julia Brandes. Scott T. Parsell. "The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces." Algebra Number Theory 15 (9) 2289 - 2314, 2021. https://doi.org/10.2140/ant.2021.15.2289
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