Ramanujan's Lost Notebook

Berndt, Bruce C.; Kim, Byungchan; Yee, Ae Ja

doi:10.1007/978-1-4614-3810-6

Cited by 134 publications

(36 citation statements)

References 55 publications

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“…The internal sums in the r.h.s. may be computed using the identity in Entry 6.3.1 of Ramunjan's lost notebook (see [70] The r.h.s. may be expanded as …”

Section: D1 Expansion Of 1/θ In Ramanujan's Partial Thetasmentioning

confidence: 99%

Superconformal index, BPS monodromy and chiral algebras

Cecotti

Song

Vafa

et al. 2017

J. High Energ. Phys.

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We show that specializations of the 4d N = 2 superconformal index labeled by an integer N is given by Tr M N where M is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras A N . This generalizes the recent results for the N = −1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S 2 × T 2 where we turn on 1 2 N units of U(1) r flux on S 2 .

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“…The internal sums in the r.h.s. may be computed using the identity in Entry 6.3.1 of Ramunjan's lost notebook (see [70] The r.h.s. may be expanded as …”

Section: D1 Expansion Of 1/θ In Ramanujan's Partial Thetasmentioning

confidence: 99%

Superconformal index, BPS monodromy and chiral algebras

Cecotti

Song

Vafa

et al. 2017

J. High Energ. Phys.

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“…The Rogers-Fine identity has had a variety of applications to q-series and the theory of partitions; see [1], [4] and [8]. It is interesting to note that Ramanujan must have known this identity even though he never wrote it down in full.…”

Section: Euler Uses the Identitymentioning

confidence: 99%

Euler’s Pentagonal Number Theorem and the Rogers-Fine Identity

Andrews

Bell

2012

Ann. Comb.

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Abstract. Euler discovered the pentagonal number theorem in 1740 but was not able to prove it until 1750. He sent the proof to Goldbach and published it in a paper that finally appeared in 1760. Moreover, Euler formulated another proof of the pentagonal number in his notebooks theorem around 1750. Euler did not publish this proof or communicate it to his correspondents, probably because of the difficulty of clearly presenting it with the notation at the time. In this paper we show that the method of Euler's unpublished proof can be used to give a new proof of the celebrated Rogers-Fine identity.

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“…In addition, in his Lost Notebook [8], [10] Ramanujan found q series identities such as [8; p. 57 (1 − q 2 )(1 − q 4 ) · · · (1 − q 2 n)…”

Section: Introductionmentioning

confidence: 99%

Parity in partition identities

Andrews¹

2013

Combinatory Analysis

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Abstract. This paper considers a variety of parity questions connected with classical partition identities of Euler, Rogers, Ramanujan and Gordon. We begin by restricting the partitions in the Rogers-Ramanujan-Gordon identities to those wherein even parts appear an even number of times. We then take up questions involving sequences of alternating parity in the parts of partitions. This latter study leads to: (1) a bi-basic q-binomial theorem and q-binomial series, (2) a new interpretation of the Rogers-Ramanujan identities, and (3) a new natural interpretation of the fifth-order mock theta functions f 0 (q) along with a new proof of the Hecke-type series representation.

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Ramanujan's Lost Notebook

Cited by 134 publications

References 55 publications

Superconformal index, BPS monodromy and chiral algebras

Superconformal index, BPS monodromy and chiral algebras

Euler’s Pentagonal Number Theorem and the Rogers-Fine Identity

Parity in partition identities

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