Abstract
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. When restricted to Chen cones, it reduces to Connes and Kreimer’s Algebraic Birkhoff Factorisation for maps with values in the algebra of ordinary meromorphic functions in one variable.
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Guo, L., Paycha, S., Zhang, B. (2017). Renormalised conical zeta values. In: Fauvet, F., Manchon, D., Marmi, S., Sauzin, D. (eds) Resurgence, Physics and Numbers. CRM Series, vol 20. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-613-1_7
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DOI: https://doi.org/10.1007/978-88-7642-613-1_7
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-612-4
Online ISBN: 978-88-7642-613-1
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