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31: 1.9 Calculus of a Complex Variable

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Jordan Curve Theorem

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32: 19.17 Graphics

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Figure 19.17.7: Cauchy principal value of $R_J(0.5,y,1,p)$ for $y=0,\mathrm{\hspace{0.17em}0.01},\mathrm{\hspace{0.17em}0.05},\mathrm{\hspace{0.17em}0.2},\mathrm{\hspace{0.17em}1}$, . …As $p\to 0$ the curve for $y=0$ has the finite limit $-8.10386\mathrm{\dots }$; see (19.20.10). Magnify

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33: 19.25 Relations to Other Functions

… ►The sign on the right-hand side of (19.25.35) will change whenever one crosses a curve on which , for some $j$. … ►The sign on the right-hand side of (19.25.40) will change whenever one crosses a curve on which , for some $j$. …

34: 23.22 Methods of Computation

… ►Suppose that the invariants $g_2=c$, $g_3=d$, are given, for example in the differential equation (23.3.10) or via coefficients of an elliptic curve (§23.20(ii)). …

35: Bibliography E

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Notes:

Links to software for elliptic curve methods of factorization and primality testing.

External Links:

Home Page

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4th item.

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36: 22.3 Graphics

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Figure 22.3.2: $k=0.7$, $-3K\le x\le 3K$, $K=1.8456\mathrm{\dots }$. For $\mathrm{cn}(x,k)$ the curve for $k=1/\sqrt{2}=0.70710\mathrm{\dots }$ is a boundary between the curves that have an inflection point in the interval $0\le x\le 2K\left(k\right)$, and its translates, and those that do not; see Walker (1996, p. 146). Magnify

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37: Bibliography

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Algorithm 39: Areas under the normal curve. The Computer Journal 12 (2), pp. 197–198.

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Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

Document

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§7.25(ii).

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38: Bibliography D

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Computing Riemann matrices of algebraic curves. Phys. D 152/153, pp. 28–46.

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External Links:

ISSN 0167-2789, Document, MathReview (John B. Little), ZentralBlatt

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3rd item.

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39: Bibliography G

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Riemann surfaces, plane algebraic curves and their period matrices. J. Symbolic Comput. 26 (6), pp. 789–803.

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External Links:

ISSN 0747-7171, Document, MathReview (Gabino González Díez), ZentralBlatt

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1st item.

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40: Bibliography K

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Introduction to Elliptic Curves and Modular Forms. 2nd edition, Graduate Texts in Mathematics, Vol. 97, Springer-Verlag, New York.

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External Links:

ISBN 0-387-97966-2, MathReview, ZentralBlatt

Referenced by:

§20.10(i), §20.12(i), §20.9(iii), §22.18(iv), §23.1, §23.20(ii), §23.20(v), Ch.23.

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