Tootfinder

This https://arxiv.org/abs/2505.00489 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Weighted averages of $\operatorname{SL}_2(\mathbb{R})$ automorphic kernel, Part I: non-oscillatory functions
We prove a theorem that evaluates weighted averages of sums parametrised by congruence subgroups of $\operatorname{SL}_2(\mathbb{Z})$. In the proof, spectral methods are applied directly to the automorphic kernel instead of going over sums of Kloosterman sums. In number theoretical applications this better preserves the specific symmetries throughout the application of spectral methods. In a separate paper we apply the main theorem to quadratic polynomials and obtain new results about their gre…

Theoretical modeling of QCD radiation in off-shell Higgs production through gluon fusion
Rafael Coelho Lopes de S\'a, Martina Javurkova, Matteo Lazzeretti, Raoul R\"ontsch
https://arxiv.org/abs/2506.17022

Theoretical modeling of QCD radiation in off-shell Higgs production through gluon fusion
The measurement of the Higgs boson width is a critical test of the Standard Model, with significant implications for understanding electroweak symmetry breaking. Direct measurements are limited by detector resolution, but it can be measured with greater precision through a combined analysis of on-shell and off-shell Higgs boson production. While results for on-shell production have been computed to a very high accuracy, theoretical predictions for off-shell Higgs boson production are not as wel…

Limiting distributions of ratios of Binomial random variables
Adriel Barretto, Zachary Lubberts
https://arxiv.org/abs/2506.13071 https://

Limiting distributions of ratios of Binomial random variables
We consider the limiting distribution of the quantity $X^s/(X+Y)^r$, where $X$ and $Y$ are two independent Binomial random variables with a common success probability and a number of trials $n$ and $m$, respectively, and $r,s$ are positive real numbers. Under several settings, we prove that this converges to a Normal distribution with a given mean and variance, and demonstrate these theoretical results through simulations.