Concept
Bernhard Riemann
Publications associées (37)
Some algebro-geometric solutions for the coupled modified Kadomtsev-Petviashvili equations arising from the Neumann type systems
A treatment is described for getting some algebro-geometric solutions of the coupled modified Kadomtsev-Petviashvili (cmKP) equations and a hierarchy of 1 + 1 dimensional integrable nonlinear evolution equations (INLEEs) by using the Neumann type systems t ...
American Institute of Physics2012On equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis
By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to ...
Springer US2012Finite Element Method on Riemann Surfaces and Applications to the Laplacian Spectrum
The objective of this PhD thesis is the approximate computation of the solutions of the Spectral Problem associated with the Laplace operator on a compact Riemann surface without boundaries. A Riemann surface can be seen as a gluing of portions of the Hype ...
EPFL2012On the second successive minimum of the Jacobian of a Riemann surface
To a compact Riemann surface of genus g can be assigned a principally polarized abelian variety (PPAV) of dimension g, the Jacobian of the Riemann surface. The Schottky problem is to discern the Jacobians among the PPAVs. Buser and Sarnak showed that the s ...
Springer Netherlands2012Capacities, Systoles and Jacobians of Riemann Surfaces
To any compact Riemann surface of genus g one may assign a principally polarized abelian variety (PPAV) of dimension g, the Jacobian of the Riemann surface. The Jacobian is a complex torus and we call a Gram matrix of the lattice of a Jacobian a period Gra ...
EPFL2011Fixed point free involutions on Riemann surfaces
In this paper, involutions without fixed points on hyperbolic closed Riemann surface are discussed. For an orientable surface X of even genus with an arbitrary Riemannian metric d admitting an involution tau, it is known that min (p is an element of X) d(p ...
The Hebrew University Magnes Press, Springer2008Trace coordinates of Teichmüller spaces of Riemann surfaces
Using an algebraic formalism based on matrices in SL(2,R), we explicitly give the Teichmüller spaces of Riemann surfaces of signature (0,4) (X pieces), (1,2) ("Fish" pieces) and (2,0) in trace coordinates. The approach, based upon gluing together two build ...
EPFL2006Resolving the wave vector in negative refractive index media
We address the general issue of resolving the wave vector in complex electromagnetic media including negative refractive media. This requires us to make a physical choice of the sign of a square root imposed merely by conditions of causality. By considerin ...
Optical Society of America2005Some remarks on the uniformizing function in genus 2
The authors propose a numerical method for the uniformization of Riemann surfaces and algebraic curves in genus two with highly accurate results. Let be a Fuchsian group acting on the unit disk , and let . It is well known that $S ...
Kluwer Academic Publishers, Springer2005