Search
Search Results
-
The Modified Π-Riemann Sums
In Chap. 4 we introduce the modified Π–Riemann sums. Some of the applications discussed include ψ–asymptotically distributed sequences, uniformly...
-
A Modern View of the Riemann Integral
This monograph uncovers the full capabilities of the Riemann integral. Setting aside all notions from Lebesgue’s theory, the author embarks on an...
-
The origin and developments of Kurzweil’s generalized Riemann integral
The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further...
-
Lattice Sums of Hyperplane Arrangements
The aim of the present chapter is to prove Theorems 9.10 , 9.11 ,...
-
The Riemann Hypothesis As the Parity of Special Binomial Coefficients
AbstractThe Riemann hypothesis has many equivalent reformulations. Some of them are arithmetical, that is, they are statements about properties of...
-
Five Hilbert Space Models Related to the Riemann Zeta Function
In a recent work of the author, a de Branges space was constructed, as well as an operator on it whose spectrum coincides with the set of nontrivial...
-
Formulas for p-adic q-integrals including falling-rising factorials, combinatorial sums and special numbers
The main purpose of this paper is to provide a novel approach to deriving formulas for the p -adic q -Volkenborn integral including the Volkenborn...
-
Coda
In Chap. 7 we discuss briefly the extension of our results to the context of Riemann–Stieltjes integrals, and we also touch briefly on modified...
-
Riemann-Hilbert problems and soliton solutions of nonlocal reverse-time NLS hierarchies
The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrödinger (NLS)...
-
Sequential generalized Riemann–Liouville derivatives based on distributional convolution
Sequential generalized fractional Riemann–Liouville derivatives are introduced as composites of distributional derivatives on the right half axis and...
-
The Pattern and Uniform Integrals
In Chap. 5 we introduce the pattern and uniform integrals. Whereas the original applications of the pattern integrals were limited to summability...
-
Efficient GPU Implementation of Multidimensional Incomplete Riemann Solvers for Hyperbolic Nonconservative Systems: Applications to Shallow Water Systems with Topography and Dry Areas
This paper deals with a class of efficient, genuinely two-dimensional Riemann solvers for hyperbolic nonconservative systems. A particularity of...
-
Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums
We investigate the number of steps taken by three variants of the Euclidean algorithm on average over Farey fractions. We show asymptotic formulae...
-
On the Generalized Li’s Criterion Equivalent to the Riemann Hypothesis and Its First Applications
We present some new results and first applications of the recently established by us (Ukrainian Math. J. 2014, 66, pp. 371–383) generalized Li’s...
-
The Riemann Map** Theorem
In his Göttingen dissertation of 1851 Bernhard Riemann enunciated (p. 40 of his Werke, 1953 ed.) and attempted to prove the famous theorem that now...
-
Further Apéry-Like Series for Riemann Zeta Function
AbstractBy means of two transformation formulas of classical hypergeometric series, several Apéry-like series involving harmonic numbers of higher...