27 citations · 52 across the 9 of their papers we have counts for
9 papers
On Sun's Conjectures for Truncated Jacobi-Symbol Determinants via Supersingular Elliptic Curves
Guo Li, Xiaoju Yan
We study the truncated Jacobi-symbol determinants proposed by Zhi-Wei Sun in \cite{ZWSun} and…
A note on connected cofiltered coalgebras, conilpotent coalgebras and Hopf algebras
Xing Gao, Li Guo
This notes gives a proof that a connected coaugmented cofiltered coalgebra is a conilpotent coalgebra and thus a connected coaugmented cofiltered bialgebra is a Hopf algebra. This…
Renormalisation and locality: branched zeta values
Pierre Clavier, Li Guo, Sylvie Paycha +1
Multivariate renormalisation techniques are implemented in order to build, study and then renormalise at the poles, branched zeta functions associated with trees. For this purpose,…
Renormalised conical zeta values
Li Guo, Sylvie Paycha, Bin Zhang
Conical zeta values associated with rational convex polyhedral cones generalise multiple zeta values. We renormalise conical zeta values at poles by means of a generalisation of Co…
Rota's Classification Problem, rewriting systems and Gröbner-Shirshov bases
Xing Gao, Li Guo
In this paper we revisit Rota's Classification Problem on classifying algebraic identities for linear operator. We reformulate Rota's Classification Problem in the contexts of rewr…
Counting an infinite number of points: a testing ground for renormalization methods
Li Guo, Sylvie Paycha, Bin Zhang
This is a leisurely introductory account addressed to non-experts and based on previous work by the authors, on how methods borrowed from physics can be used to "count" an infinite…
Averaging algebras, Schröder numbers, rooted trees and operads
Li Guo, Jun Pei
In this paper, we study averaging operators from an algebraic and combinatorial point of view. We first construct free averaging algebras in terms of a class of bracketed words cal…
Algebraic Birkhoff Factorization and the Euler-Maclaurin Formula on Cones
Li Guo, Sylvie Paycha, Bin Zhang
We equip the space of lattice cones with a coproduct which makes it a connected cograded colagebra. The exponential sum and exponential integral on lattice cones can be viewed as l…
Conical zeta values and their double subdivision relations
Li Guo, Sylvie Paycha, Bin Zhang
We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of m…