3 papers
math.CA2026
Reinforcing a Philosophy: A counting approach to square functions over local fields
Kirsti D. Biggs, Julia Brandes, Kevin Hughes
In this paper, we study square functions for extension operators over finite-type, planar curves endowed with the Euclidean arclength measure. We prove new results for curves of th…
math.NT2026
Structure and paucity in affine diagonal systems, I
Julia Brandes, Trevor D. Wooley
Let and . We show that whenever is large and the system \[ x_1^j+x_2^j-y_1^j-y_2^j=h_j\quad (j=1,2,3) \] has more than …
math.NT2025
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…