Tootfinder

Some Bounds Related to the 2-adic Littlewood Conjecture
Dinis Vitorino, Ingrid Vukusic
https://arxiv.org/abs/2506.04110 https://arxiv…

Some Bounds Related to the 2-adic Littlewood Conjecture
For every irrational real $α$, let $M(α) = \sup_{n\geq 1} a_n(α)$ denote the largest partial quotient in its continued fraction expansion (or $\infty$, if unbounded). The $2$-adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational $α$ such that $M(2^k α)$ is uniformly bounded by a constant $C$ for all $k\geq 0$. Badziahin proved (considering a different formulation of 2LC) that if a counterexample exists, then the bound $C$ is at least $8$. We improve this bou…

This https://arxiv.org/abs/2409.11082 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Most totally real fields do not have universal forms or Northcott property
We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott property, is meager. The main tool is a new theorem on the number of square classes of totally positive units represented by a quadratic lattice of a given rank.

Lie Group Theory of Multipole Moments and Shape of Stationary Rotating Fluid Bodies
Sergei M. Kopeikin (University of Missouri-Columbia, USA)
https://arxiv.org/abs/2505.14712

Lie Group Theory of Multipole Moments and Shape of Stationary Rotating Fluid Bodies
We present a rigorous framework for determining the equilibrium configurations of uniformly rotating, self-gravitating fluid bodies. This work addresses the classical challenge of modeling rotational deformation in celestial objects such as stars and planets. By integrating foundational theory with modern mathematical tools, we develop a unified formalism that enhances the precision and generality of shape modeling in astrophysical contexts. Our method applies Lie group theory to vector flows a…