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2016

Renormalised conical zeta values

Guo, Li, Paycha, Sylvie, Zhang, Bin

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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 Connes and Kreimer's Algebraic Birkhoff Factorisation.
This paper serves as a motivation for and an application of this generalised renormalisation scheme.
The latter also yields an Euler-Maclaurin formula on rational convex polyhedral lattice cones which relates exponential sums to exponential integrals.

Renormalised conical zeta values · Around

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A. Connes and D. Kreimer, Hopf algebras, Renormalisation and Noncommutative Geometry, Comm. Math. Phys
1988
Earlier work this paper cites.
L. Guo and B. Zhang, Renormalisation of multiple zeta values J. Algebra
2008
Earlier work this paper cites.

Similar

L. Guo and B. Zhang, Differential Birkhoff decomposition and renormalisation of multiple zeta values, J. Number Theory
2008
Cited alongside, same era.
D. Manchon, Hopf algebras, from basics to applications to renormalisation, Comptes-rendus des Rencontres mathématiques de Glanon
2008
Cited alongside, same era.
L. Guo, S. Paycha and B. Zhang, Residue of meromorphic functions with linear poles, preprint
Cited in the paper.
L. Guo, S. Paycha and B. Zhang, Algebraic Birkhoff Factorisation and the Euler-Maclaurin formula on cones, arXiv:1306.3420
Original
Cited in the paper.
L. Guo, S. Paycha and B. Zhang, Counting an infinite number of points: a testing ground for renormalisation methods, arXiv:1501.00429
Original
Cited in the paper.

Then

D. Manchon and S. Paycha, Nested sums of symbols and renormalised multiple zeta values, Int. Math. Res. Papers 2010 issue 24, 4628-4697 (2010)
2010
Later among the works it cites.
L. Guo, S. Paycha and B. Zhang, Conical zeta values and their double subdivision relations, Adv. Math
2014
Later among the works it cites.

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