Representation of Squares by Nonsingular Cubic Forms
arXiv:2204.09396 · doi:10.1007/s11856-021-2116-2
Abstract
We prove an asymptotic formula for the number of representations of squares by nonsingular cubic forms in six or more variables. The main ingredients of the proof are Heath-Brown's form of the Circle Method and various exponential sum results. The depth of the exponential sum results is comparable to Hooley's work on cubic forms in nine variables, in particular we prove an analogue of Katz' bound.
29 pages. Arxiv upload of older paper. Published in Isr. J. Math