相关论文: Analytic continuation of multiple polylogarithms
This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…
Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning…
Multiplication of polynomials is among key operations in computer algebra which plays important roles in developing techniques for other commonly used polynomial operations such as division, evaluation/interpolation, and factorization. In…
We construct polylogarithms on families of pointed Riemann surfaces of any genus which describe monodromies of meromorphic connections with simple poles. Furthermore, we show that the polylogaritms are computable as power series in…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…
We generalize the definition of the polylogarithm classes to the case of commutative group schemes, both in the sheaf theoretic and the motivic setting. This generalizes and simplifies the existing cases.
We describe maximal, in a sense made precise, analytic continuations of germs at infinity of unary functions definable in the o-minimal structure R_an,exp on the Riemann surface of the logarithm. As one application, we give an upper bound…
In this talk, we discuss recent progress in the application of generalizations of polylogarithms in the symbolic computation of multi-loop integrals. We briefly review the Maple program MPL which supports a certain approach for the…
We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation
By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…
We discuss a new approach to realization of the well-known Weierstrass's programme on efficient continuation of an analytic element corresponding to a~multivalued analytic function with finite number of branch points. Our approach is based…
We present analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg. The calculation is based on the Simplified Differential Equations approach.…
We construct an effective algorithmic method to compute the homological monodromy of a complex polynomial which is tame. As an application we show the existence of conjugated polynomials in a number field which are not topologically…
We review recent developments in the study of multiple polylogarithms, including the Hopf algebra of the multiple polylogarithms and the symbol map, as well as the construction of single valued multiple polylogarithms and discuss an…
We give an efficient algorithm to enumerate all sets of $r\ge 1$ quadratic polynomials over a finite field, which remain irreducible under iterations and compositions.
Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…
Let $X$ be a complex manifold and $f\colon X\to \C^p$ a holomorphic mapping defining a complete intersection. We prove that the iterated Mellin transform of the residue integral associated to $f$ has an analytic continuation to a…