Corpus ID: 221555752

Families of eulerian functions involved in regularization of divergent polyzetas

@article{Bui2020FamiliesOE,
  title={Families of eulerian functions involved in regularization of divergent polyzetas},
  author={V. Bui and V. H. N. Minh and Q. H. Ng{\^o}},
  journal={arXiv: Number Theory},
  year={2020}
}
Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton-Girard identity) for the complex Gamma function, we are interested in the ratios of $\zeta(2k)/\pi^{2k}$ and their multiindexed generalization, we will obtain an analogue situation and draw some consequences about a structure of the algebra of polyzetas values, by means of some combinatorics of noncommutative rational… Expand
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References

SHOWING 1-10 OF 26 REFERENCES
Independence of Hyperlogarithms over Function Fields via Algebraic Combinatorics
TLDR
This work obtains a necessary and sufficient condition for the linear independence of solutions of differential equations for hyperlogarithms and extends the property of linear independence to the largest known ring of coefficients. Expand
Summations of polylogarithms via evaluation transform
In this work, the Evaluation transform is adapted to interpret the polylogarithms as being the Evaluation of the words yxn, for meromorphic kernels and meromorphic inputs. The functional equations onExpand
Sweedler's duals and Schützenberger's calculus
TLDR
A rational calculus is created which can be applied to harness Sweedler's duals for bialgebras and which is eventually illustrated on an example. Expand
A localized version of the basic triangle theorem
TLDR
A localized version of the basic triangle theorem is given in order to prove the independence of hyperlogarithms over various function fields and provides direct access to rings of scalars and avoids the recourse to fraction fields as that of meromorphic functions for instance. Expand
Dual bases for noncommutative symmetric and quasi-symmetric functions via monoidal factorization
TLDR
An effective variation of Schutzenberger's factorization adapted to the diagonal pairing between a graded space and its dual is used to propose effective constructions of dual bases for the noncommutative symmetric and quasi-symmetric functions. Expand
Free Lie algebras
My principal references are [Serre:1965], [Reutenauer:1993], and [de Graaf:2000]. My interest in free Lie algebras has been motivated by the well known conjecture that Kac-Moody algebras can beExpand
Fonctionnelles causales non linaires et indtermines non commutatives
— Thé foundations ofa theory of non-lmear causal functionals are laid down using non-commutative indeterminates.
Commutative Algebra I
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed
On the solutions of universal differential equation with three singularities, in Confluentes
  • Mathematici, Tome
  • 2019
...
1
2
3
...