An incomplete Riemann Zeta function as a fractional integral [PDF]
arXivAn incomplete Riemann zeta function can be expressed as a lower-bounded, improper Riemann-Liouville fractional integral, which, when evaluated at $0$, is equivalent to the complete Riemann zeta function. Solutions to Landau's problem with $\zeta(s) = \eta(s)/0$ establish a functional relationship between the Riemann zeta function and the Dirichlet eta ...
arxiv
Riemann hypothesis and some new asymptotically multiplicative integrals which contain the remainder of the prime-counting function $π(x)$ [PDF]
arXiv, 2010 A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.
arxiv
On Riemann-Liouville integral of ultra-hyperbolic type [PDF]
, 1964 Yasuo Nozaki
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The One‐Dimensional Coulomb Hamiltonian: Properties of Its Birman–Schwinger Operator
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The objective of the present paper is to study in detail the properties of the Birman–Schwinger operator for a self‐adjoint realization of the one‐dimensional Hamiltonian with the Coulomb potential, both when the Hamiltonian is defined only on ℝ+$$ {\mathbb{R}}_{+} $$ and when it is defined on the whole real line.
S. Fassari +4 more
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Three‐dimensional lattice ground states for Riesz and Lennard‐Jones–type energies
Studies in Applied Mathematics, Volume 150, Issue 1, Page 69-91, January 2023., 2023 Abstract The Riesz potential fs(r)=r−s$f_s(r)=r^{-s}$ is known to be an important building block of many interactions, including Lennard‐Jones–type potentials fn,mLJ(r):=ar−n−br−m$f_{n,m}^{\rm {LJ}}(r):=a r^{-n}-b r^{-m}$, n>m$n>m$ that are widely used in molecular simulations.
Laurent Bétermin +2 more
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On weighted Montogomery identities for Riemann-Liouville fractional integrals [PDF]
Konuralp Journal of Mathematics, 1(1), 2013, 2012 In this paper, we extend the weighted Montogomery identities for the Riemann-Liouville fractional integrals. We also use this Montogomery identities to establish some new Ostrowski type integral inequalities.
arxiv
On the almost‐circular symplectic induced Ginibre ensemble
Studies in Applied Mathematics, Volume 150, Issue 1, Page 184-217, January 2023., 2023 Abstract We consider the symplectic‐induced Ginibre process, which is a Pfaffian point process on the plane. Let N be the number of points. We focus on the almost‐circular regime where most of the points lie in a thin annulus SN$\mathcal {S}_{N}$ of width O1N$O\left(\frac{1}{N}\right)$ as N→∞$N \rightarrow \infty$. Our main results are the bulk scaling
Sung‐Soo Byun, Christophe Charlier
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Singular integrals and estimates for the Cauchy-Riemann equations [PDF]
, 1973 E. M. Stein
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Integral inequalities for s-convexity via generalized fractional integrals on fractal sets [PDF]
arXiv, 2019 In this study, we establish a new integral inequalities of Hermite-Hadamard type for $s$-convexity via Katugampola fractional integral. This generalizes the Hadamard fractional integrals and Riemann-Liouville into a single form. We show that the new integral inequalities of Hermite-Hadamard type can be obtained via the Riemann-Liouville fractional ...
arxiv