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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational points and homogeneous spaces over function fields of curves
曲线函数场 有理点 齐次空间
2023/4/17
In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
Twisted Weyl Group Multiple Dirichlet Series Over the Rational Function Field
Rational Function Field Multiple Dirichlet
2014/12/8
Let K be a global field. For each prime p of K, the p-part of a multiple Dirichlet series defined over K is a generating function in several variables for the p-power coefficients. Let _ be an irreduc...
J.Ritt [1] has investigated the structure of complex polynomials with respect to superposition.
The polynomial P(x) is said to be indecomposable iff the representation P = P1 ◦ P2 means that
e...
Hilbert series of PI relatively free G-graded algebras are rational functions
free G-graded algebras rational functions
2010/11/19
Let G be a finite group, (g_{1},...,g_{r}) an (unordered) r-tuple of G^{(r)} and x_{i,g_i}'s variables that correspond to the g_i's, i=1,...,r. Let F be the corresponding free...
Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves
Cartan geometry holomorphic connection Calabi–Yau manifold rational curve
2010/12/14
We prove that if a Calabi–Yau manifold M admits a holomorphic Cartan geometry, then M is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on com...
Bernstein type inequality in monotone rational approximation
Bernstein type inequality monotone rational approximation
2010/12/10
The following analog of Bernstein inequality for monotone rational functions is established: if R is an increasing on [−1, 1] rational function of degree n, then R′(x) < 9n 1 − x2 kRk, x ∈...
A formula for the HOMFLY polynomial of rational links
formula for the HOMFLY polynomial rational links
2010/12/3
In this paper we give an explicit formula for the HOMFLY polynomial of a rational link (in particular, knot) in terms of a special continued fraction for the rational number that defines the given lin...
Complexity of Creative Telescoping for Bivariate Rational Functions
Hermite reduction creative telescoping
2013/9/3
The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger’s framework of (differential) creative telescoping. Our c...
INTRODUCTION.Itisthepurposeofthispapertopresentsomeresults,ontheproblemofinterpolationandapproximationtoafunctiouf(z),analyticonaclosedlimitedpointsetEinthecomplexz-planewhosecomplementKisconnectedand...