Exponential sums over singular binary quintics

TL;DR

This paper estimates exponential sums over singular binary quintic forms using Waring decomposition, extending previous methods from binary quartics to a more complex space.

Contribution

It introduces a characteristic-free estimate for exponential sums over singular binary quintic forms, expanding the applicability of previous techniques.

Findings

Provides a characteristic-free estimate of exponential sums over singular binary quintics.

Extends methods from binary quartics to binary quintics, a non-coregular space.

Abstract

We give an estimate of exponential sums over singular binary quintic forms in a characteristic-free form, based on the Waring decomposition of binary forms. This extends the method on our preceding result on the space of binary quartics to a non-coregular space.