Related papers: Pseudodifferential arithmetic and the Riemann hypo…

I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.

The Lie algebras over the algebra of dual numbers are introduced and investigated.

In this paper a new integral for the remainder of $\pi(x)$ is obtained. It is proved that there is an infinite set of the formulae containing miscellaneous parts of this integral.

The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the…

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

This short note presents a peculiar generalization of the Riemann hypothesis, as the action of the permutation group on the elements of continued fractions. The problem is difficult to attack through traditional analytic techniques, and…

We settled a conjecture of Feigin, Wang and Yoshinaga, appeared in the preprint "Integral expressions for derivations of multiarrangements" (arXiv: 2309.01287v2).

The purpose of this paper is to make an introduction to univalent function theory for readers of any level, assuming only foundational knowledge in real and complex analysis. In particular, we state and proof (with details) important…

The paper presents two arithmetical versions of the Nyman-Beurling equivalence with the Riemann hypothesis, proved by classical, quasi elementary, number-theoretic methods, based on an integrated version of the classical combinatorial…

We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.

We survey the classical results of the Dirichlet Approximation Theorem.

This paper has been withdrawn by the author(s), due to the existence of a much better paper in http://arxiv.org/abs/cs.CR/0207027

This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long…

In this revised version, we add some expository material and references and make some minor corrections.

These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.

We furnish an explicit bound for the prime number theorem in short intervals on the assumption of the Riemann hypothesis.

In the paper, we first prove a sufficient condition for the Riemann hypothesis which involves the order of magnitude of the partial sum of the Liouville function. Then we show a formula which is curiously related to the proved sufficient…

We report the emergence of a striking new phenomenon in arithmetic, which we call murmurations. First observed experimentally through averages over large arithmetic datasets, murmurations can be detected and analyzed using standard…

The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…

In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.