Vassiliev invariants and a strange identity related to the Dedekind eta-function

By Don Zagier. 2001

248 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3acfca19ecab52e72a1d3c3e3551667b0373f15d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Problems on invariants of knots and 3-manifolds (2004, background): “Furthermore, Zagier [410] showed that ∞ ∑”
q-Dedekind type sums related to q-zeta function and basic L-series☆ (2006, unknown): “In [36], Zagier studied q-series and Dedekind eta-function.”
Quantum modular forms (2010, background): “We will be fairly brief in our treatment here, since this function was studied in detail in [15], and will only discuss the quantum modular aspect.”
Cyclotomic Completions of Polynomial Rings (2002, background): “Zagier [13] studied the series ∑ n≥0(q)n, which was introduced by Kontsevich, and observed that it can be expanded in q − ζ for any root ζ of unity.”
Unearthing the visions of a master: harmonic Maass forms and number theory (2008, unknown): “…Hikami, Kac, Lawrence, Malmendier, Mellit, Okada, Wakimoto, and Zagier [15] [18] [21] [26] [92] [120] [121] [122] [130] [131] [144] [152] [153] [211] apply this theory to: • Donaldson invariants • Gauge theory • Representation theory of Lie superalgebras • Knot theory • Mathematical physics •…”
Partial theta functions and mock modular forms as q-hypergeometric series (2011, methodology): “[26] D. Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function.”
Torus knots and quantum modular forms (2014, methodology): “A celebrated example is the Kontsevich-Zagier series [29]”
MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS (2013, background): “Similar theorems have been previously discovered by Zagier and others (for example, see [6, 21, 29, 31, 32, 41]).”
Asymptotic expansions of certain partial theta functions (2011, methodology): “Connection with certain L-series and partitions It is now well known that we can possibly use partial theta function identities to obtain generating functions for certain L-functions; for example, see [3] and [10].”
Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations (2008, background): “This series has already been shown by Zagier [13] to count certain chord diagrams, or involutions, introduced by Stoimenow [12] to give upper bounds on the dimension of the space of Vassiliev’s knot invariants of a given degree.”