Related papers: A note on the Artin Conjecture

We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.

In this summary paper, we present the key ideas behind the recent proof of the $K(\pi, 1)$ conjecture for affine Artin groups, which states that complements of locally finite affine hyperplane arrangements with real equations and stable…

A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…

The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators of any Artin group generate an obvious right-angled Artin subgroup. We consider a larger set of elements consisting of all the centers of the…

In this survey paper we study Manin's Conjecture from a geometric perspective. The focus of the paper is the recent conjectural description of the exceptional set in Manin's Conjecture due to Lehmann-Sengupta-Tanimoto. After giving an…

We make the final step to give a proof for the Brannan's conjecture. The basic tool of the study is a Mac-Laurin development and an adequately estimation of an integral.

This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.

In this review, I discuss briefly theoretical scenarios concerning the interpretation of recent results from indirect and direct dark matter searches, with emphasis on the former.

We introduce a number field analogue of the Mertens conjecture and demonstrate its falsity for all but finitely many number fields of any given degree. We establish the existence of a logarithmic limiting distribution for the analogous…

We extend the notions of quasi-monomial groups and almost monomial groups, in the framework of supercharacter theories, and we study their connection with Artin's conjecture regarding the holomorphy of Artin $L$-functions.

We obtain average results on the Sato-Tate conjecture for elliptic curves for small angles.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

In this paper, we give a simple counter example to the famous Hodge conjecture.

The covering properties of Artinian rings which depend on their additive structure only, are investigated.

We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.

We present a short review of the existing evidence in favor of neutrino mass and neutrino oscillations which come from different kinds of experiments. We focus our attention in particular on solar neutrinos, presenting a global updated…

The article presents the proof of Casas-Alvero conjecture.

In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.

We present new infinite arctangent sums and infinite sums of products of arctangents. Many previously known evaluations appear as special cases of the general results derived in this paper.