Related papers: A problem of Polya

We offer a more general Bailey pair than one that was proved in two different papers by two different methods [5, 12].

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

In this paper we proved a new numerically explicit version of the P\'{o}lya--Vinogradov inequality. Our proof is based on the new ideas of V.A. Bykovskii and improves a recent inequality obtained by C. Pomerance.

Under the Riemann Hypothesis, we improve the error term in the asymptotic formula related to the counting lattice problem studied in a first part of this work. The improvement comes from the use of Weyl's bound for exponential sums of…

In this paper we give a generalization of a result of Wei.

Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy-like inequalities and formulate an open problem for the…

We present inequalities and some applications to Kellers' limit and Carlemans' inequality.

We study several consequences of the packing problem, a conjecture from combinatorial optimization, using algebraic invariants of square-free monomial ideals. While the packing problem is currently unresolved, we successfully settle the…

In this note we prove an inequality involving primes and the product of consecutive primes.

We give a more detailed description of the new system of Pl\"ucker-like equations from [4], discuss how it relates to the usual Pl\"ucker equations, and correct a mistake in that article.

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

In this note we obtain a new convergence result for the Adomian decomposition method.

Motivated by the study of simultaneous cores, we give three proofs (in varying levels of generality) for the expected norm of a weight in a highest weight representation of a complex simple Lie algebra. First, we argue directly using the…

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.

In this short note, we improve the famous Reid Inequality related to linear operators.

We prove an extension of the Thue-Vinogradov Lemma and show some applications. This paper is another example for the application of the polynomial method.

We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional…

We prove Polya's conjecture of 1943: For a real entire function of order greater than 2, with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tends to infinity with n. We use the saddle point method and…

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

A separated sequence $\Lambda$ on the real line is called a Polya sequence if any entire function of zero exponential type bounded on $\Lambda$ is constant. In this paper we solve the problem by Polya and Levinson that asks for a…