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  Asymptotics of Nahm sums at roots of unity

Garoufalidis, S., & Zagier, D. (2021). Asymptotics of Nahm sums at roots of unity. Ramanujan Journal, 55(1), 219-238. doi:10.1007/s11139-020-00266-x.

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 Creators:
Garoufalidis, Stavros1, Author           
Zagier, Don1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Geometric Topology, High Energy Physics - Theory
 Abstract: We give a formula for the radial asymptotics to all orders of the special $q$-hypergeometric series known as Nahm sums at complex roots of unity. This result is used in~\cite{CGZ} to prove one direction of Nahm's conjecture
relating the modularity of Nahm sums to the vanishing of a certain invariant in $K$-theory. The power series occurring in our asymptotic formula are identical to the conjectured asymptotics of the Kashaev invariant of a knot once we convert Neumann-Zagier data into Nahm data, suggesting a deep connection
between asymptotics of quantum knot invariants and asymptotics of Nahm sums
that will be discussed further in a subsequent publication.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 1812.07690
DOI: 10.1007/s11139-020-00266-x
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Title: Ramanujan Journal
  Abbreviation : Ramanujan J
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 55 (1) Sequence Number: - Start / End Page: 219 - 238 Identifier: -