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This note started out as a letter to J\"urgen Ritter and is brief attempt to entice some number theorists to study hom-Lie algebras.
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
In this electronic appendix to our paper "Input Invariants," accepted at ESEC/FSE'22, we provide additional examples, formal definitions, theorems, and proof sketches to complement our paper. Furthermore, we show the invariants that ISLearn…
Lieberman and Melott built their recent arXiv preprint 0704.2896 on my published paper and (a preprint of) a subsequent comment by Liebermans associate Cornette. But had this group waited for the Cornette comment to actually appear in print…
An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the…
There were some errors in paper hep-th/9303018 in formulas 6.1, 6.6, 6.8, 6.11. These errors have been corrected in the present version of this paper. There are also some minor changes in the introduction.
We give a short Wiener measure proof of the Riemann hypothesis based on a surprising, unexpected and deep relation between the Riemann zeta $\zeta(s)$ and the trivial zeta $\zeta_{t}(s):=Im(s)(2Re(s)-1)$.
The arXiv has collected 1.5 million pre-print articles over 28 years, hosting literature from scientific fields including Physics, Mathematics, and Computer Science. Each pre-print features text, figures, authors, citations, categories, and…
We provide the first experimental results on non-synthetic datasets for the quasi-diagonal Riemannian gradient descents for neural networks introduced in [Ollivier, 2015]. These include the MNIST, SVHN, and FACE datasets as well as a…
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…
The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more…
Ballantine--Beck--Feigon--Maurischat introduced the subsum polynomial \[ \operatorname{sp}(\lambda,x):=\prod_i (1+x^{\lambda_i}) \] attached to an integer partition $\lambda$, and studied rational functions obtained by summing reciprocals…
We decide to combine this preprint with two other ones (arXiv:1101.1946 and arXiv:1008.3887). The results on Apery numbers and polynomials will be added to the new version of arxiv:1101.1946, and those results on generalized trinomial…
The aim of this paper is to propose an ``elementary" approach to Coleman's theory of p-adic abelian integrals. Our main tool is a theory of commutative p-adic Lie groups (the logarithm map); we use neither dagger analysis nor…
In this paper we present a concise mathematical description of active inference in discrete time. The main part of the paper serves as a basic introduction to the topic, including a detailed example of the action selection mechanism. The…
This preprint is dedicated to a self contained simple proof of the classical criteria for representability of algebraic functions of several complex variables by radicals. It also contains a criteria for representability of algebroidal…
Schleischitz [arXiv:1701.01129] determined exponents of best approximations to a strong Liouville number by integer polynomials and algebraic numbers of precribed degree. In this note, we show that we cannot extend his result to arbitrary…
This is an exposition, in 12 pages including all prerequisites and a generalization, of Karamata's little known elementary proof of the Landau-Ingham Tauberian theorem, a result in real analysis from which the Prime Number Theorem follows…
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.