by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...

in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.

LetQ be a connected and simply connected domain on the Riemann sphere, not coinciding with the Riemann sphere and with the whole complex plane C. Then, according to the Riemann Theorem, there exists a conformal bijection between Q and the exterior of the unit disk. In this paper we find an explicit form of this map for a broad class of domains with analytic boundaries. 2000 Math. Sabj. Class. 3...

In the earlier study of Riemann surfaces, one was interested in the embeddability of Riemann surfaces in Euclidean spaces. Complex Analysists showed that any Riemann surface can be embedded in Euclidean 3-space. But recently, this problem has been conveyed to the problem in the Riemannian manifolds. In this paper we investigate the history and very recent results of problem in affordable and sy...

Riemann introduced his surfaces in the middle of the 19th century in order to “geometrize” complex analysis. In doing so, he paved the way for a great deal of modern mathematics such as algebraic geometry, manifold theory, and topology. So this would certainly be of interest to students in these areas, as well as in complex analysis or number theory. In simple terms, a Riemann surface is a surf...

Given a holomorphic vector bundle E : EX → X over a compact Kähler manifold, one introduces twisted GW-invariants of X replacing virtual fundamental cycles of moduli spaces of stable maps f : Σ → X by their cap-product with a chosen multiplicative characteristic class of H(Σ, fE)− H(Σ, fE). Using the formalism [17] of quantized quadratic hamiltonians, we express the descendent potential for the...

The confluence of computer science and quantum mechanics has inspired a proof of the Riemann Hypothesis for the discrete geometric (Clifford) algebras Cl(n,0) over Z3 = {0,1,−1}, as expected from the Weil Conjectures. The symptoms of Riemann Fever are clearly evident here long periods of apathy punctuated by febrile investigations lasting from minutes to (here, two) weeks, accompanied by altern...

We use discrete analogs of Riemann–Hilbert problem’s methods to derive the discrete Bessel kernel which describes the poissonized Plancherel measures for symmetric groups. To do this we define a discrete analog of 2 by 2 Riemann–Hilbert problems of special type. We also give an example, explicitly solvable in terms of classical special functions, when a discrete Riemann–Hilbert problem converge...