The f(q) mock theta function conjecture and partition ranks

Bringmann, Kathrin; Ono, Ken

doi:10.1007/s00222-005-0493-5

Cited by 187 publications

(258 citation statements)

References 22 publications

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“…that numerous other relations exist analogous to (12)- (19), and in particular M (1, 11, 11n + 1) = M (2, 11, 11n + 1) = M (3, 11, 11n + 1) = M (4, 11, 11n + 1); that M (m, 11, n) has a generating function not completely different in form from (24);…”

Section: Hold In Factmentioning

confidence: 97%

Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks

Andrews

2007

Invent. math.

171

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Atkin and Garvan introduced the moments of ranks of partitions in their work connecting ranks and cranks. Here we consider a combinatorial interpretation of these moments. This requires the introduction of a new representation for partitions, the Durfee symbol, and subsequent refinements. This in turn leads us to a variety of new congruences for our 'marked' Durfee symbols much in the spirit of Dyson's original conjectures on the ranks of partitions.

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Section: Hold In Factmentioning

confidence: 97%

Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks

Andrews

2007

Invent. math.

171

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“…The vacua of the SO.3/-Donaldson theory with 2N f massless monopoles are given by a smooth connection where " is the universal bundle introduced in (5). " has the total Chern class c."…”

Section: Donaldson Theory With Monopolesmentioning

confidence: 99%

SO(3)–Donaldson invariants of ℂP²and mock theta functions

Malmendier

Ono

2012

Geom. Topol.

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We compute the Moore-Witten regularized u-plane integral on CP 2 , and we confirm the conjecture that it is the generating function for the SO.3/-Donaldson invariants of CP 2 . We also derive generating functions for the SO.3/-Donaldson invariants with 2N f massless monopoles using the geometry of certain rational elliptic surfaces (N f 2 f0; 2; 3; 4g), and we show that the partition function for N f D 4 is nearly modular. Our results rely heavily on the theory of mock theta functions and harmonic Maass forms (for example, see Ono [40]). 57R57

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“…Remark: We briefly discuss the convergence in Proposition 3.1 for weight 1/2 harmonic weak Maass forms. To show this, we need similar estimates for sums of the Kloosterman sums as in theorem 4.1 of the paper by Bringmann and Ono (14). In that work, the Kloosterman sums were rewritten as Salie-type sums, which were then estimated using the equidistibution of CM points [similar results may also be found in the paper by Duke (16)].…”

Section: Poincaré Seriesmentioning

confidence: 88%

Ramanujan’s mock theta functions

Griffin

Ono

Rolen

2013

Proc. Natl. Acad. Sci. U.S.A.

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In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function , and he offered some alleged examples. Recent work by Zwegers [Zwegers S (2001) Contemp Math 291:268–277 and Zwegers S (2002) PhD thesis (Univ of Utrecht, Utrecht, The Netherlands)] has elucidated the theory encompassing these examples. They are holomorphic parts of special harmonic weak Maass forms. Despite this understanding, little attention has been given to Ramanujan’s original definition. Here, we prove that Ramanujan’s examples do indeed satisfy his original definition.

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The f(q) mock theta function conjecture and partition ranks

Cited by 187 publications

References 22 publications

Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks

Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks

SO(3)–Donaldson invariants of ℂP²and mock theta functions

Ramanujan’s mock theta functions

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The f(q) mock theta function conjecture and partition ranks

Cited by 187 publications

References 22 publications

Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks

Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks

SO(3)–Donaldson invariants of ℂP2and mock theta functions

Ramanujan’s mock theta functions

Contact Info

Product

Resources

About

SO(3)–Donaldson invariants of ℂP²and mock theta functions