Related papers: On Hall-Littlewood polynomials

In this paper I prove a conjecture which gives a lower bound for the largest absolute value of the coefficients of the n-th cyclotomic polynomial for some n. Moreover this estimate is essentially sharp.

We establish an inequality of different metrics for algebraic polynomials.

A short note on bounds on distance to variety of a point in terms of the Taylor coefficients at the point.

This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.

We relate the combinatorics of Hall-Littlewood polynomials to that of abelian $p$-groups with alternating or Hermitian perfect pairings. Our main result is an analogue of the classical relationship between the Hall algebra of abelian…

New cases of the multiplicity conjecture are considered.

We study a natural analogue of Collatz's Conjecture for polynomials over $\mathbb{F}_2$.

We study an inequality suggested by Littlewood, our result refines a result of Bennett.

The paper presents a counterexample to the Hodge conjecture.

In this paper, we gave some properties of binomial coefficient.

Some Open Problems Concerning Orthogonal Polynomials.

We prove two new summation formulae of Hall-Littlewood polynomials over partitions into bounded parts and derive some new multiple $q$-identities of Rogers-Ramanujan type.

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

We obtain simple proofs of certain inequalites for bivariate means.

We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polynomial, Proc. Amer. Math. Soc., 148 (2020] 1429 -- 1437].

In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to…

In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials

We give a closed formula of the Littlewood-Richardson coefficients.

The notion of multipolynomials was recently introduced and explored by T. Velanga in [10] as an attempt to encompass the theories of polynomials and multi- linear operators. In the present paper we push this subject further, by proving…

We prove a binomial formula for Macdonald polynomials and consider applications of it.