15 citations · 21 across the 7 of their papers we have counts for
8 papers
On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer
V. C. Bui, V. Hoang Ngoc Minh, V. Nguyen Dinh +1
This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations () using our recent results on combinatorial aspects of zeta functions on several va…
On the solutions of universal differential equation by noncommutative Picard-Vessiot theory
V. C. Bui, V. Hoang Ngoc Minh, V. Nguyen Dinh +1
Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursiv…
A local Theory of Domains and its (Noncommutative) Symbolic Counterpart
V. C. Bui, G. H. E. Duchamp, V. Hoang Ngoc Minh +2
It is widely accepted nowadays that polyzetas are connected by polynomial relations. One way to obtain relations among polyzetas is to consider their generating series and the rela…
Families of eulerian functions involved in regularization of divergent polyzetas
V. C. Bui, V. Hoang Ngoc Minh, V. Nguyen Dinh +1
Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton-Gi…
Kleene stars of the plane, polylogarithms and symmetries
Gérard Henry Edmond Duchamp, Vincel Hoang Ngoc Minh, Ngo Quoc Hoan
We extend the definition and construct several bases for polylogarithms Li T , where T are some series, recognizable by a finite state (multiplicity) automaton of alphabet 4 X = {x…
Mathematical renormalization in quantum electrodynamics via noncommutative generating series
Gérard Henry Edmond Duchamp, Vincel Hoang Ngoc Minh, Quoc Hoan Ngo +2
In this work, we focus on on the approach by noncommutative formal power series to study the combinatorial aspects of the renormalization at the singularities in …
Harmonic sums and polylogarithms at non-positive multi-indices
Gérard Duchamp, Hoang Ngoc, Ngo Quoc
Extending Eulerian polynomials and Faulhaber's formula 1, we study several combi-natorial aspects of harmonic sums and polylogarithms at non-positive multi-indices as well as their…
(Pure) transcendence bases in -deformed shuffle bialgebras
Van Chiên Bui, Gérard H. E. Duchamp, Quoc Hoan Ngô +2
Computations with integro-differential operators are often carried out in an associative algebra with unit, and they are essentially non-commutative computations. By adjoining a co…