Related papers: Large Sieve Inequalities for Special Characters to…
Let $x=a+ib$ be a complex number, so we have the following inequality $$(1/\sqrt{2})|a+b|\leq |x|\leq |a|+|b|$$ We give an operator version of above inequality. Also we obtain some results for normal operators.
We establish an explicit inequality for the number of divisors of an integer $n$. It uses the size of $n$ and its number of distinct prime divisors.
In this paper, we establish some new Ostrowski type inequalities for the class of h-convex functions which are super-multiplicative or super-additive and nonnegative. Some applications for special means and PDF's are given.
An exponent of distribution 1/16 is established for square-free palindromes. The main input is an upper bound for the number of palindromes, in arithmetic progressions to large moduli, divisible by large squares. Our argument combines a…
We study in this article a new pointwise estimate for ''rough'' singular integral operators. From this pointwise estimate we will derive Sobolev type inequalities in a variety of functional spaces.
We propose various strategies for improving the computation of discrete logarithms in non-prime fields of medium to large characteristic using the Number Field Sieve. This includes new methods for selecting the polynomials; the use of…
In this paper, we introduce concise expressions for the complex Bessel integral that enables us to improve the spectral large sieve inequality of Watt for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$. Our result…
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
Here we demonstrate a sieve for analysing primes and their composites, using equivalence classes based on the modulo 6 return value as applied to the Natural numbers. Five features of this 'Hexile' sieve are reviewed. The first aspect, is…
We give conditions characterizing equality in the Minkowski inequality for big divisors on a projective variety. Our results draw on the extensive history of research on Minkowski inequalities in algebraic geometry.
We present a new sieve that allows us to find the prime numbers by using only regular patterns and, more importantly, avoiding any duplication of elements between them.
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
In this paper, some new inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are convex and applications for special means are given. Finally, some error estimates for the trapezoidal formula are…
Let S be a smooth minimal complex projective surface of maximal Albanese dimension. Under the assumption that the canonical class of S is ample and the irregularity of S, q(S), is greater or equal to 5 we show that K^2>=…
In this paper, we obtain some Simpson type inequalities for functions whose derivatives in absolute value are $\varphi$-convex.
Some sharp Bessel type inequalities for non-orthonormal families of vectors in inner product spaces are given. Applications for complex numbers are also provided.
In this paper, we study the uniform dimension and the associated prime ideals of induced modules over skew PBW extensions.
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.
Some inequalities for different types of convexity are established.
We establish sharp convolution and multiplication estimates in weighted Lebesgue, Fourier Lebesgue and modulation spaces. Especially we recover some known results.