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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.NT2024
Local analysis of the Kuznetsov formula and the density conjecture
Edgar Assing, Valentin Blomer, Paul D. Nelson
We prove Sarnak's spherical density conjecture for the principal congruence subgroup of SL(n, Z) of arbitrary level. Applications include a complete version of Sarnak's optimal lif…
math.NT2024
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…