Related papers: A simplified proof of Serre's Conjectures

In this expository note, we present an approach to the generalization of Serre of the Sato-Tate Conjecture. Most of its content is taken from Serre's original references. However, we provide a few new examples and supply references to…

In this note we provide a simple formula of general term of recurrent sequence.

The goal of this note is to study the smallest conic singular value of a matrix from a Lagrangian duality viewpoint and provide an efficient method for its computation.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.

This article gives a self-contained proof of Mostow Rigidity, at least modulo undergrad real analysis. The proof should be accessible to grad students interested in geometry and topology. It has no new research, but I think that this is an…

In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.

The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.

New cases of the multiplicity conjecture are considered.

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.

We give a proof of the o-minimal version of the Whitney Extension Theorem simplified as compared to the original ones. A new simplifying ingredient is a definable variant of Urysohn's lemma for class $\mathcal{C}^q$ (see Section 3).

The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…

The notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…

We recently formulated important Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Modular Johnson-Lindenstrauss Flattening Conjecture in the Appendix of \textit{[arXiv: 2207.12799.v1]}. For the sake of wide accessibility…

Let F be a totally real field and p an odd prime. If r is a continuous, semisimple, totally odd mod p representation of the absolute Galois group of F which is tamely ramified at all places of F dividing p, then we formulate a conjecture…

In this paper we present a short and elementary proof for the error in Simpson's rule.

We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

Conditions for Bayesian posterior robustness have been examined in recent literature. However, many of the proofs seem to be long and complicated. In this paper, we first summarize some basic lemmas that have been applied implicitly or…

In this paper, we prove a minimal modularity lifting theorem for Galois representations (conjecturally) associated to Siegel modular forms of genus two which are holomorphic limits of discrete series at infinity.