3 papers
math.NT2026
Values of ternary quadratic forms at integers and the Berry-Tabor conjecture for 3-tori
Wooyeon Kim, Jens Marklof, Matthew Welsh
Berry and Tabor conjectured in 1977 that spectra of generic integrable quantum systems have the same local statistics as a Poisson point process. We verify their conjecture in the…
math.NT2025
The distribution of intersections in and lattices related to roots of cubic congruences
Matthew Welsh
In this note we study the distribution of the intersections between certain translates of closed orbits of the positive diagonal subgroup in $\mathrm{SL}(3, \mathbb{Z}) \backslash…
math.NT2021
Bounds for theta sums in higher rank I
Jens Marklof, Matthew Welsh
Theta sums are finite exponential sums with a quadratic form in the oscillatory phase. This paper establishes new upper bounds for theta sums in the case of smooth and box truncati…