Related papers: Another Riemann-Farey Computation

An approach to constructing an upper bound for the Riemann-Farey sum is described.

We develop a method for calculating Riemann sums using Fourier analysis.

An open problem concerning Riemann sums, posed by O. Furdui, is considered.

In the paper we prove a new upper bound for Heilbronn's exponential sum and obtain some applications of our result to distribution of Fermat quotients.

Certain new inequalities for the sums of factorials are presented.

We establish upper bounds for moments of zeta sums using results on shifted moments of the Riemann zeta function under the Riemann hypothesis.

We improve the previuosly known bound for some vertex Folkman numbers.

In this short note, we obtain error estimates for Riemann sums of some singular functions.

A proposed solution to the Riemann Hypothesis

We establish a new lower bound for Mathieu's series and present a new derivation of its expansions in terms of Riemann Zeta functions.

In this paper, we consider certain finite sums related to the "largest odd divisor", and we obtain, using simple ideas and recurrence relations, sharp upper and lower bounds for these sums.

Explicit estimates for the Riemann zeta-function on the $1$-line are derived using various methods, in particular van der Corput lemmas of high order and a theorem of Borel and Carath\'{e}odory.

Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…

In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.

Under the Riemann hypothesis, we use the distribution of zeros of the zeta function to get a lower bound for the maximum of some derivative of Hardy's function.

In the paper, some lower bounds for polygamma functions are refined.

Computer-based attempts to construct lower bounds for small Ramsey numbers are discussed. A systematic review of cyclic Ramsey graphs is attempted. Many known lower bounds are reproduced. Several new bounds are reported.

An elementary method for computing various prime sequences using the sequence of Farey sequences is described.

The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more…

In this paper, we will present some characterizations for the upper bound of the Bakry-Emery curvature on a Riemannian manifold by using functional inequalities on path space. Moreover, some characterizations for general lower and upper…