相关论文: Another Riemann-Farey Computation

We provide explicit upper bounds of the order $\log t/\log\log t$ for $|\zeta'(s)/\zeta(s)|$ and $|1/\zeta(s)|$ when $\sigma$ is close to $1$. These improve existing bounds for $\zeta(s)$ on the $1$-line.

In this note, we describe an interpretation of the (continuous) Fourier transform from the perspective of the Chinese Remainder Theorem. Some related issues, including a new derivation of Poisson summation formula, are discussed.

We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.

In this paper, we obtain a sharp upper bound for the sum of the first $k$-th eigenvalues for this Dirichlet problem of poly-Laplacian with any order, which is viewed as an extension of the result due to Cheng and Wei (Journal of…

We consider some properties of integrals considered by Hardy and Koshliakov, and which have also been further extended recently by Dixit. We establish a new general integral formula from some observations about the digamma function. We also…

In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this…

We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we…

A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.

We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.

We construct a non - improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand.

We consider several differential-topological invariants of compact 4-manifolds which directly arise from Riemannian variational problems. Using recent results of Bauer and Furuta, we compute these invariants in many cases that were…

In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.

We give an elementary proof for new strict upper and lower bounds for the correction term in Ramanujan's approximation for the factorial function

We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…

An introduction and overview of constructive reverse mathematics.

We propose a simple derivation of an upper bound for the perimeter of an ellipse. The procedure, which relies on the use of elliptic integrals, consists in introducing, via inequalities and convexity properties, specific integrals which can…

In an earlier paper we introduced the notion of 'bifurcating continued fractions' in a heuristic manner. In this paper a formal theory is developed for the 'bifurcating continued fractions'.

By modifying Cole's example, we construct explicit Riemann surfaces with large bounds on corona solutions in an elementary way.

We find an explicit upper bound for general $L$-functions on the critical line, assuming the Generalized Riemann Hypothesis, and give as illustrative examples its application to some families of $L$-functions and Dedekind zeta functions.…

We present some new ideas to derive {\em a priori} second order estiamtes for a wide class of fully nonlinear parabolic equations. Our methods, which produce new existence results for the initial-boundary value problems in $\bfR^n$, are…