相关论文: A Riemann-Farey Computation

Another 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.

A proposed solution to the Riemann Hypothesis

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

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

Certain new inequalities for the sums of factorials are presented.

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…

We establish an upper bound of the sum of the eigenvalues for the Dirichlet problem of the fractional Laplacian. Our result is obtained by a subtle computation of the Rayleigh quotient for specific functions.

We give a sharp upper bound for the entries of the representations of a rational number as a sum of Egyptian fractions.

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

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 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.

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

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.

In the paper, we first prove a sufficient condition for the Riemann hypothesis which involves the order of magnitude of the partial sum of the Liouville function. Then we show a formula which is curiously related to the proved sufficient…

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

Assuming the Riemann Hypothesis we establish an upper bound for the sum of the M{\" o}bius function up to $x$. Our method is based on estimating the frequency with which intervals of a given length can contain an unusual number of ordinates…

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