## 20 Citations

A FRACTIONAL NEWTON SERIES FOR THE RIEMANN ZETA FUNCTION

- Mathematics
- 2014

In recent years much attention has been given to Newton series representations of a regularized Zeta function. Such representations are limited as they do not lead to a series expansion for the Zeta…

On some expansions for the Euler Gamma function and the Riemann Zeta function

- MathematicsJ. Comput. Appl. Math.
- 2012

Finite differences of Euler's zeta function

- Mathematics
- 2017

We find accurate approximations for certain finite differences of the Euler zeta function, .x/. 2010 Mathematics Subject Classification: 41A60; 11M06; 26D15

A FRACTIONAL NEWTON SERIES FOR

- Mathematics
- 2014

In recent years much attention has been given to Newton series representations of a regularized Zeta function. Such representations are limited as they do not lead to a series expansion for the Zeta…

Acceleration Methods for Series: A Probabilistic Perspective

- Mathematics
- 2016

We introduce a probabilistic perspective to the problem of accelerating the convergence of a wide class of series, paying special attention to the computation of the coefficients, preferably in a…

Certain summation formulas involving harmonic numbers and generalized harmonic numbers

- Mathematics, PhysicsAppl. Math. Comput.
- 2011

Differential calculus for linear operators represented by finite signed measures and applications

- Mathematics
- 2013

We introduce a differential calculus for linear operators represented by a family of finite signed measures. Such a calculus is based on the notions of g-derived operators and processes and…

Some summation formulas involving harmonic numbers and generalized harmonic numbers

- Mathematics, PhysicsMath. Comput. Model.
- 2011

Discretized Keiper/Li Approach to the Riemann Hypothesis

- MathematicsExp. Math.
- 2020

The Keiper–Li sequence is deformated to fully explicit sequences, simpler to analyze and to compute, thus it can be demonstrated explicit tests that selectively react to zeros off the critical line.

Note on two extensions of the classical formula for sums of powers on arithmetic progressions

- Mathematics
- 2017

We give two extensions of the classical formula for sums of powers on arithmetic progressions. This is achieved by using an identity involving binomial mixtures, which can be viewed as a…

## References

SHOWING 1-10 OF 42 REFERENCES

The Theory of the Riemann Zeta-Function

- Mathematics
- 1987

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects…

On Maslanka's Representation for the Riemann Zeta Function

- MathematicsInt. J. Math. Math. Sci.
- 2010

A rigorous proof is given of the hypergeometric-like representation of the Riemann zeta function 𝜁(𝑠) discovered by Maslanka as a series of Pochhamer polynomials with coefficients depending on the…

Sharpenings of Li's Criterion for the Riemann Hypothesis

- Mathematics
- 2006

Exact and asymptotic formulae are displayed for the coefficients λn used in Li's criterion for the Riemann Hypothesis. For n → ∞ we obtain that if (and only if) the Hypothesis is true, λn ∼ n(A log n…

Toward Verification of the Riemann Hypothesis: Application of the Li Criterion

- Mathematics
- 2005

We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence {λk}, which are certain logarithmic derivatives of the Riemann xi…

Continued Fractions, Comparison Algorithms, and Fine Structure Constants

- Computer Science
- 2000

A light tour of dynamical systems (symbolic dynamics), number theory (continued fractions), special functions, special functions (multiple zeta values), functional analysis (transfer operators), numerical analysis (series acceleration), and complex analysis (the Riemann hypothesis) contribute to a detailed characterization of the complexity of comparison and sorting algorithms.

Hypergeometric-like Representation of the Zeta-Function of Riemann

- Mathematics
- 2001

We present a new expansion of the zeta-function of Riemann. The current formalism -- which combines both the idea of interpolation with constraints and the concept of hypergeometric functions -- can,…

Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work

- Mathematics
- 1978

The Indian mathematician Ramanujan Ramanujan and the theory of prime numbers Round numbers Some more problems of the analytic theory of numbers A lattice-point problem Ramanujan's work on partitions…

The Positivity of a Sequence of Numbers and the Riemann Hypothesis

- Mathematics
- 1997

Abstract In this note, we prove that the Riemann hypothesis for the Dedekind zeta function is equivalent to the nonnegativity of a sequence of real numbers.

The Calculus of Finite Differences

- MathematicsNature
- 1934

THE last edition of Boole's “Finite Differences” appeared in 1880, and was in fact a reprint of the edition of 1872. The interval of sixty years has seen in the elementary field Sheppard's…