18 citations · 42 across the 19 of their papers we have counts for
4 papers · 1 filter
Rational lines on cubic hypersurfaces II
Julia Brandes, Rainer Dietmann, David B. Leep
We show that any rational cubic hypersurface of dimension at least 33 defined over a number field vanishes on a -rational projective line, reducing the previous lower bound…
A minimalist version of the circle method and Diophantine problems over thin sets
Kirsti D. Biggs, Julia Brandes
This paper studies the minimal conditions under which we can establish asymptotic formulae for Waring's problem and other additive problems that may be tackled by the circle method…
Local mean value estimates for Weyl sums
Julia Brandes, Changhao Chen, Igor E. Shparlinski
We obtain new estimates - both upper and lower bounds - on the mean values of the Weyl sums over a small box inside of the unit torus. In particular, we refine recent conjectures o…
Campana points on diagonal hypersurfaces
Francesca Balestrieri, Julia Brandes, Miriam Kaesberg +3
We construct an integral model for counting Campana points of bounded height on diagonal hypersurfaces of degree greater than one, and give an asymptotic formula for their number,…