# Goldbach conjecture

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## 1—10 of 22 matching pages

##### 1: 27.13 Functions

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###### §27.13(ii) Goldbach Conjecture

… ►Goldbach’s assertion is that $S(n)\ge 1$ for all even $n>4$. 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 $c$. …##### 2: 18.38 Mathematical Applications

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►was used in de Branges’ proof of the long-standing Bieberbach conjecture concerning univalent functions on the unit disk in the complex plane.
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##### 3: 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 …##### 4: David M. Bressoud

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► 227, in 1980, Factorization and Primality Testing, published by Springer-Verlag in 1989,

*Second Year Calculus from Celestial Mechanics to Special Relativity*, published by Springer-Verlag in 1992,*A Radical Approach to Real Analysis*, published by the Mathematical Association of America in 1994, with a second edition in 2007, Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, published by the Mathematical Association of America and Cambridge University Press in 1999, A Course in Computational Number Theory (with S. …##### 5: Bibliography Y

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Partitions with difference conditions and Alder’s conjecture.
Proc. Natl. Acad. Sci. USA 101 (47), pp. 16417–16418.
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##### 6: 21.9 Integrable Equations

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►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).
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##### 7: 17.14 Constant Term Identities

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###### Zeilberger–Bressoud Theorem (Andrews’ $q$-Dyson Conjecture)

… ►Macdonald (1982) includes extensive conjectures on generalizations of (17.14.1) to root systems. These conjectures were proved in Cherednik (1995), Habsieger (1986), and Kadell (1994); see also Macdonald (1998). …##### 8: Richard A. Askey

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►This inequality was a key element of Louis de Branges’ proof of the Bieberbach conjecture in 1985.
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##### 9: 17.13 Integrals

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►Askey (1980) conjectured extensions of the foregoing integrals that are closely related to Macdonald (1982).
These conjectures are proved independently in Habsieger (1988) and Kadell (1988).

##### 10: Bibliography K

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A proof of Askey’s conjectured
$q$-analogue of Selberg’s integral and a conjecture of Morris.
SIAM J. Math. Anal. 19 (4), pp. 969–986.
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A proof of the $q$-Macdonald-Morris conjecture for $B{C}_{n}$
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Mem. Amer. Math. Soc. 108 (516), pp. vi+80.
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Special functions and the Bieberbach conjecture.
Amer. Math. Monthly 95 (8), pp. 689–696.
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