Search
Search Results
-
On the Representation of Integers as Sums of a Class of Triangular Numbers
AbstractIn this paper, we discuss the problem of the number of representations of positive integers as sums of triangular numbers. The method we...
-
An Arithmetical Function Related to Báez-Duarte’s Criterion for the Riemann Hypothesis
In this mainly expository article, we revisit some formal aspects of Báez-Duarte’s criterion for the Riemann hypothesis. In particular, starting from...
-
Rational functions, cotangent sums and Eichler integrals
With the help of so called pre-weak functions, we formulate a very general transformation law for some holomorphic functions on the upper half plane...
-
Sums of Independent Random Variables
The classical large-sample theory is about the sum of independent random variables. Even though large-sample techniques have expanded well beyond the...
-
On a Method for Solving a Mixed Boundary Value Problem for a Parabolic Equation Using Modified Sinc-Approximation Operators
AbstractA new method is proposed for obtaining a generalized solution of a mixed boundary value problem for a parabolic equation with boundary...
-
Introduction
Bernhard Riemann Riemann, B submitted his Habilitationsschrift—the postdoctoral examination required to qualify to lecture at a university—to the...
-
Application of Caputo Fractional Operator to Analyse the Fractional Model of Brain Tumour Via Modified Technique
In this article, the fractional model of brain tumour is investigated. The numerical solution of this model is obtained by the modified technique...
-
The Riemann hypothesis
In zeta functionRiemann|( Riemannzeta function|( his famous paper on the zeta function [120], Riemann remarked that it is likely that all the...
-
Phase Operator on \(L^2(\mathbb {Q}_p)\) and the Zeroes of Fisher and Riemann
The distribution of the non-trivial zeroes of the Riemann zeta function, according to the Riemann hypothesis, is tantalisingly similar to the zeroes...
-
Analytical Solution of Time Fractional Kawahara and Modified Kawahara Equations by Homotopy Analysis Method
The article covers the implementation of the Homotopy Analysis method (HAM) in order to derive the general estimated analytical solutions for the...
-
Composition-theoretic series in partition theory
We use sums over integer compositions analogous to generating functions in partition theory, to express certain partition enumeration functions as...
-
Descriptions of fractional coefficients of Jacobi polynomial expansions
In this paper, we express the expansion coefficients of the Jacobi polynomial series expansion in terms of the Hankel transform, and expand functions...
-
Vanishing Magnetic Field Limits of Solutions to the Isentropic Chaplygin Gas Magnetogasdynamics Equations
We investigate the vanishing magnetic field limits of Riemann solutions to the isentropic Chaplygin gas magnetogasdynamics equations. It is...
-
Energy distribution of harmonic 1-forms and Jacobians of Riemann surfaces with a short closed geodesic
We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the...
-
On the Riemann Zeta Function and Gaussian Multiplicative Chaos
We review some aspects of the statistical behavior of the Riemann zeta function on the critical line. Especially, we discuss how its functional...
-
Further preliminaries
This chapter introduces topics needed in some of the subsequent chapters: Möbius transformations, hyperbolic geometry, normal families, the Riemann...
-
Boundedness of the Hilbert Transform in Besov Spaces
Boundedness conditions are found for the Hilbert transform H in Besov spaces with Muckenhoupt weights. The operator H in this situation acts on...
-
