Related papers: The Kronecker limit formulas via the distribution …

We prove that the solution of the Kac analogue of Boltzmann's equation can be viewed as a probability distribution of a sum of a random number of random variables. This fact allows us to study convergence to equilibrium by means of a few…

Kronecker's 1856 paper contains a solvability theorem that is useful to construct unsolvable algebraic equations. We show how Kronecker's solvability theorem can be derived naturally via a polynomial complete decomposition method. This…

We construct p-adic families of Klingen Eisenstein series and L-functions for cuspforms (not necessarily ordinary) unramified at an odd prime p on definite unitary groups of signature (r, 0) (for any positive integer r) for a quadratic…

We generalize current known distribution results on Shanks--R\'enyi prime number races to the case where arbitrarily many residue classes are involved. Our method handles both the classical case that goes back to Chebyshev and function…

We introduce partially lax limits of infinity-categories, which interpolate between ordinary limits and lax limits. Most naturally occurring examples of lax limits are only partially lax; we give examples arising from enriched categories…

A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.

The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…

Let p be a prime number which is split in an imaginary quadratic field k. Let \mathfrak{p} be a place of k above p. Let k_\infty be the unique Z_p-extension of k which unramified outside of \mathfrak{p}, and let K_\intfy be a finite…

We establish effective convergence rates in the Doeblin-Lenstra law, describing the limiting distribution of approximation coefficients arising from continued fraction convergents of a typical real number. More generally, we prove…

We prove the Lindeberg--Feller central limit theorem without using characteristic functions or Taylor expansions, but instead by measuring how far a distribution is from the standard normal distribution according to the $2$-Wasserstein…

We carry out "Hecke summation" for the classical Eisenstein series $E_k$ in an adelic setting. The connection between classical and adelic functions is made by explicit calculations of local and global intertwining operators and Whittaker…

In the present paper we discuss how to generalize ``Quantum-Classical Correspondence'' by means of the notion of interacting Fock spaces, which associates algebraic probability theory and the theory of orthogonal polynomials of probability…

Let $p$ be a prime number. The $p$-power cyclic resultant of a polynomial is the determinant of the Sylvester matrix of $t^{p^n}-1$ and the polynomial. It is known that the sequence of $p$-power cyclic resultants and its non-$p$-parts…

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of…

Formulas are derived for counting walks in the Kronecker product of graphs, and the associated spectral distributions are obtained by the Mellin convolution of probability distributions. Two-dimensional restricted lattices admitting the…

We study multivariate generalizations of the $q$-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely…

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

We explore the computational content of Kronecker's lemma via the proof-theoretic perspective of proof mining and utilise the resulting finitary variant of this fundamental result to provide new rates for the Strong Law of Large Numbers for…

In this paper we consider $q$-state potential on general infinite trees with a nearest-neighbor $p$-adic interactions given by a stochastic matrix. {We show the uniqueness of the associated Markov chain ({\em splitting Gibbs measures})…

We obtain statistical results on the possible distribution of all partial sums of a Kloosterman sum modulo a prime, by computing explicitly the support of the limiting random Fourier series of our earlier functional limit theorem for…