Related papers: Inequalities for exponential sums
We improve constants in the Rademacher-Menchov inequality.
We have fundamentally corrected the proofs of the theorems from our paper [9] by giving an entirely different approach, using quite a simple method based on applications of some elementary inequalities, well-known H\"older's inequality, and…
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
We prove inequalities on symmetric tensor sums of positive definite operators. In particular, we prove multivariable operator inequalities inspired by generalizations to the well-known Hlawka and Popoviciu inequalities. As corollaries, we…
Some improvements of the celebrated Schwarz inequality in complex inner product spaces are given. Applications for n-tuples of complex numbers are provided.
A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.
We examine exponential sums of the form $\sum_{n \le X} w(n) e^{2\pi i\alpha n^k}$, for $k=1,2$, where $\alpha$ satisfies a generalized Diophantine approximation and where $w$ are different arithmetic functions that might be multiplicative,…
The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. This is achieved by establishing an improvement on…
We consider two recent conjectures of Harrington, Henninger-Voss, Karhadkar, Robinson and Wong concerning relationships between the sum index, difference index and exclusive sum number of graphs. One conjecture posits an exact relationship…
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.
In this paper we give alternate proofs of some well-known matrix inequalities. In particular, we show that under certain conditions the inequality holds \begin{align}\sum \limits_{\lambda_i\in \mathrm{Spec}(ab^{T})}\mathrm{min}\{\log…
Let $p$ be a large prime number and $g$ be any integer of multiplicative order $T$ modulo $p$. We obtain a new estimate of the double exponential sum $$ S=\sum_{n\in \mathcal{N}}\left|\sum_{m\in \mathcal{M} }e_p(an g^{m})\right|, \quad \gcd…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…
The paper discusses the summability of formal solutions of some linear q-difference-differential equations, and improves the previous result in [Tahara-Yamazawa, Opsucula Math. 35 (2015), 713-738].
We obtain general estimates for exponential integrals of the form \[ E_f(y)=\int_{\mathbb{Z}_{p}^{n}}\psi(\sum_{j=1}^r y_j f_j(x))|dx|, \] where the $f_j$ are restricted power series over $\mathbb{Q}_p$, $y_j\in\mathbb{Q}_p$, and $\psi$ a…
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic, but supply strong information when one is only a little into the upper tail. We…
In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zheng on the single variable case. As an application, for…