48 citations · 147 across the 10 of their papers we have counts for
10 papers
Quadratic residue patterns, algebraic curves and a K3 surface
Valentina Kiritchenko, Michael Tsfasman, Serge Vladuts +1
Quadratic residue patterns modulo a prime are studied since 19th century. In the first part we extend existing results on the number of consecutive -tuples of quadratic resid…
Quadratic residue patterns and point counting on K3 surfaces
Valentina Kiritchenko, Mikhail Tsfasman, Serge Vladuts +1
Quadratic residue patterns modulo a prime are studied since 19th century. We state the last unpublished result of Lydia Goncharova, reformulate it and prior results in terms of alg…
Curves of infinite genus I Riemann--Roch theorem for small degree
Ilya Zakharevich
The most useful and interesting line bundles over algebraic curves of a very high genus have the ratio δof the degree to the genus close to half-integer values, usually δ\approx 0,…
Nonlinear wave equation, nonlinear Riemann problem, and the twistor transform of Veronese webs
Ilya Zakharevich
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but i…
Kronecker webs, bihamiltonian structures, and the method of argument translation
Ilya Zakharevich
We show that manifolds which parameterize values of first integrals of integrable finite-dimensional bihamiltonian systems carry a geometric structure which we call a {\em Kronecke…
Webs, Lenard schemes, and the local geometry of bihamiltonian Toda and Lax structures
Israel M. Gelfand, Ilya Zakharevich
We introduce a criterion that a given bihamiltonian structure allows a local coordinate system where both brackets have constant coefficients. This criterion is applied to the biha…