Systems of bihomogeneous forms of small bidegree

2023/05/25 by Leonhard Hochfilzer, Hochfilzer, Leonhard · 1 citation
Mathematics · #11D45 #11D72 #11P55 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2305.16159

openalex publication_date 2023/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the circle method to count the number of integer solutions to systems of bihomogeneous equations of bidegree (1,1) and (2,1) of bounded height in lopsided boxes. Previously, adjusting Birch's techniques to the bihomogeneous setting, Schindler showed an asymptotic formula provided the number of variables grows at least quadratically with the number of equations considered. Based on recent methods by Rydin Myerson we weaken this assumption and show that the number of variables only needs to satisfy a linear bound in terms of the number of equations.

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