Related papers: A new inequality involving primes
In this paper we present many congruences for several Ap\'ery-like sequences.
In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.
In this note, we establish new an inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.
We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.
We discuss several classical and recent proofs of the isoperimetric inequality and the Sobolev inequality.
We introduce extremely symmetric primes and provide some elementary properties of these.
In this paper, a new identity for convex functions is derived. A consequence of the identity is that we can derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in…
Let $A$ be an $m\times m$ positive semidefinite block matrix with each block being $n$-square. We write $\mathrm{tr}_1$ and $\mathrm{tr}_2$ for the first and second partial trace, respectively. In this paper, we prove the following…
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
In this paper we establish a number of new estimates concerning the prime counting function \pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in…
Originally developed for measuring the heterogeneity of wealth measures, inequality indices are quantitative scores that take values in the unit interval, with the zero score characterizing perfect equality. In this paper, we draw attention…
An overview of the results of new exhaustive computations of gaps between primes in arithmetic progressions is presented. We also give new numerical results for exceptionally large least primes in arithmetic progressions.
We obtain new bounds of exponential sums modulo a prime $p$ with sparse polynomials $a_0x^{n_0} + \cdots + a_{\nu}x^{n_\nu}$. The bounds depend on various greatest common divisors of exponents $n_0, \ldots, n_\nu$ and their differences. In…
Inequalities for exponential sums are studied. Our results improve an old result of G. Halasz and a recent result of G. Kos. We prove several other essentially sharp related results in this paper.
In this paper, we propose a new primality test, and then we employ this test to find a formula for {\pi} that computes the number of primes within any interval. We finally propose a new formula that computes the nth prime number as well as…
We introduce Poincar\'e type inequalities based on rearrangement invariant spaces in the setting of metric measure spaces and analyze when they imply the doubling condition on the underline measure.
In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.
In this article we study some new pointwise inequalities between rough singular integral operators, weighted maximal functions of the gradient and weighted Morrey spaces. These pointwise estimates will naturally lead us to a new class of…
We continue our recent work on averages for ternary additive problems with powers of prime numbers.
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We…