Andrews’ q-Dyson conjecture

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21: Ranjan Roy

… ► Andrews and R. …

22: 26.21 Tables

… ►Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts $\cancel{\equiv }\pm 2(mod5)$, partitions into parts $\cancel{\equiv }\pm 1(mod5)$, and unrestricted plane partitions up to 100. …

23: Staff

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George E. Andrews, Pennsylvania State University, Chap. 17

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George E. Andrews, Pennsylvania State University

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George E. Andrews, Pennsylvania State University, for Chap. 17

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24: 27.14 Unrestricted Partitions

… ►Lehmer (1947) conjectures that $\tau \left(n\right)$ is never 0 and verifies this for all by studying various congruences satisfied by $\tau \left(n\right)$, for example: … ►For further information on partitions and generating functions see Andrews (1976); also §§17.2–17.14, and §§26.9–26.10. …

25: 17.12 Bailey Pairs

… ►See Andrews (2000, 2001), Andrews and Berkovich (1998), Andrews et al. (1999), Milne and Lilly (1992), Spiridonov (2002), and Warnaar (1998).

26: 16.23 Mathematical Applications

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§16.23(iii) Conformal Mapping

►The Bieberbach conjecture states that if ${\sum }_{n=0}^{\mathrm{\infty }}{a}_n{z}^n$ is a conformal map of the unit disk to any complex domain, then $|a_n|\le n|a_1|$. In the proof of this conjecture de Branges (1985) uses the inequality …

27: 27.13 Functions

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§27.13(ii) Goldbach Conjecture

… ►This conjecture dates back to 1742 and was undecided in 2009, although it has been confirmed numerically up to very large numbers. … ►The current status of Goldbach’s conjecture is described in the Wikipedia. … ►Hardy and Littlewood (1925) conjectures that when $k$ is not a power of 2, and that $G\left(k\right)\le 4k$ when $k$ is a power of 2, but the most that is known (in 2009) is for some constant $c$. …

28: Bibliography D

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A proof of the Bieberbach conjecture. Acta Math. 154 (1-2), pp. 137–152.

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External Links:

ISSN 0001-5962, Document, MathReview (P. L. Duren), ZentralBlatt

Referenced by:

§16.23(iii), §18.38(ii).

Encodings:

BibTeX

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Computing $\pi (x)$: The Meissel, Lehmer, Lagarias, Miller, Odlyzko method. Math. Comp. 65 (213), pp. 235–245.

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External Links:

ISSN 0025-5718, Document, MathReview (Andrew Granville), ZentralBlatt

Referenced by:

§27.18.

Encodings:

BibTeX

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29: 21.9 Integrable Equations

… ►Following the work of Krichever (1976), Novikov conjectured that the Riemann theta function in (21.9.4) gives rise to a solution of the KP equation (21.9.3) if, and only if, the theta function originates from a Riemann surface; see Dubrovin (1981, §IV.4). The first part of this conjecture was established in Krichever (1976); the second part was proved in Shiota (1986). …

30: 15.14 Integrals

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