Let 𝒪_K be the ring of integers of an imaginary quadratic field K. Recently, Ji and Xie proved that every rational map f :ℂ→ℂ of degree d ≥ 2 whose multipliers all lie in 𝒪_K is a power map, a Chebyshev map or a Lattès map. Their proof relies on a result from non-Archimedean dynamics obtained by Rivera-Letelier. In the present note, we show that one can avoid using this result by considering a differential equation instead. Our proof of Ji and Xie’s result also applies to the case of entire maps. Thus, we also show that every nonaffine entire map f :ℂ→ℂ whose multipliers all lie in 𝒪_K is a power map or a Chebyshev map.
In this paper we investigate higher moments attached to the Chebotarev Density Theorem. Our focus is on the impact that peculiar Galois group structures have on the limiting distribution. Precisely we consider in this paper the case of groups having a character of large degree. Under the Generalized Riemann Hypothesis, we prove in particular that there exists families of Galois extensions of number fields having doubly transitive Frobenius group for which no Gaussian limiting distribution occurs.
This paper presents a Lattice Boltzmann Method (LBM) tailored for solving drift-diffusion equations in cold plasma applications. The proposed scheme is aimed to be a first step to address the challenges of simulating cold plasmas, characterized by non-equilibrium conditions and complex interactions among electrons, ions, and electric fields. By employing a parabolic scaling and simplifying assumptions, the method ensures computational efficiency while maintaining accuracy. Validation is performed through numerical test cases. While promising, future work will focus on incorporating energy dynamics and handling variable diffusion coefficients to enhance the method’s applicability in diverse plasma scenarios.
A k-wise B-divisible set family is a collection F of subsets of {1,. .., n} such that any intersection of k sets in F has cardinality divisible by B. If k = B = 2, it is well-known that F <= 2tn/21. We generalise this by proving that F <= 2tn/p1 if k = B = p, for any prime number p. For arbitrary values of B, we prove that 4B2-wise B-divisible set families F satisfy F <= 2tn/& ell;1 and that the only families achieving the upper bound are atomic, meaning that they consist of all the unions of disjoint subsets of size B. This improves upon a recent result by Gishboliner, Sudakov and Timon, that arrived at the same conclusion for k-wise Bdivisible families, with values of k that behave exponentially in B. Our techniques rely heavily upon a coding-theory analogue of Kneser's Theorem from additive combinatorics. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
We give explicit characterizations of the permutations and linear isometries that leave (univariate) multiplicity codes invariant. We consider any evaluation subset of the finite field, any multiplicity and dimension, and the automorphisms are with respect to the Niederreiter-Rosenblom-Tsfasman (NRT) metric. For multiplicity one, we recover the permutation and automorphism groups of classical Reed–Solomon codes in the classical Hamming metric. In the main dimension range, automorphisms are uniquely determined by a projectivity that permutes the evaluation subset, up to multiplication by a nonzero scalar. For multiplicity one, permutations are given by affine maps that permute the evaluation subset. In contrast, for multiplicity at least two, permutations are only given by translations that permute the evaluation subset. Finally, we give an algebraic characterization of automorphisms of multiplicity codes for the folded Hamming metric.
