3 papers
cs.AI2026
First Proof
Mohammed Abouzaid, Andrew J. Blumberg, Martin Hairer +8
To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the resear…
math.NT2025
Soft bounds for local triple products and the subconvexity-QUE implication for
Paul D. Nelson
We give a soft proof of a uniform upper bound for the local factors in the triple product formula, sufficient for deducing effective and general forms of quantum unique ergodicity…
math.NT2025
Local integral transforms and global spectral decomposition
Valentin Blomer, Subhajit Jana, Paul D. Nelson
We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic -functions for Maass forms with explicit integral transfo…