Related papers: A Bernstein type inequality
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
We appended an errata to the original submission. The purpose of this errata is to point out two errors in [2] and give a weakened version of those statements made.
In this paper, we shall give an extension of operator Bellman inequality. This result is estimated via Kantorovich constant.
We prove a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms. Our results are inspired by and analogous to recent results for diagonal quadratic forms due to Bourgain.
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.
I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.
Higher order Bernstein- and Markov-type inequalities are established for trigonometric polynomials on compact subsets of the real line and algebraic polynomials on compact subsets of the unit circle. In the case of Markov-type inequalities…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
We provide a refinement of Horn's conjecture by considering spectra with repetitions. To do this we adapt P. Belkale's techniques to our context, in the form proposed by N. Berline, M. Vergne and M. Walter.
Let $f$ be a primitive form with respect to $SL_2(Z)$. Then we propose a conjecture on the congruence between the Klingen-Eisenstein lift of the Duke-Imamoglu-Ikeda lift of $f$ and a certain lift of a vector valued Hecke eigenform with…
Two types of Bernstein inequalities are established on the unit ball in $\mathbb{R}^d$, which are stronger than those known in the literature. The first type consists of inequalities in $L^p$ norm for a fully symmetric doubling weight on…
In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
We obtain inequalities of H\"{o}lder and Minkowski type with weights generalizing both the case of weights with alternating signs and the classical case of non-negative weights.
A generalization of an inequality from IMO is proven.
We look at an old conjecture of A. Tarski on cardinal arithmetic and show that if a counterexample exists, then there exists one of length omega_1 + omega .
In this paper, we develop a large sieve type inequality with characters to square moduli. One expects that the result should be weaker than the classical inequality, but, conjecturally at least, not by much. The method is generalizable to…
In this paper we obtain a partial answer to a conjecture on the solvabilty of linear difference equations in quasianalytic Carleman classes.
We survey the classical results on the prime number theorem
We resolve a conjecture of De Palma and Trevisan by proving the triangle inequality for a quantum 2-Wasserstein distance. The proof relies on complex analysis methods to establish a new integral representation of the cost in the optimal…