prime form
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11: Bibliography C
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Über die Fälle, wenn die Reihe von der Form
etc. ein Quadrat von der Form
etc. hat.
J. Reine Angew. Math. 3, pp. 89–91.
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12: 29.2 Differential Equations
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§29.2(i) Lamé’s Equation
… ►This equation has regular singularities at the points , where , and , are the complete elliptic integrals of the first kind with moduli , , respectively; see §19.2(ii). … ►§29.2(ii) Other Forms
… ►we have … ►13: 10.29 Recurrence Relations and Derivatives
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►For results on modified quotients of the form
see Onoe (1955) and Onoe (1956).
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§10.29(ii) Derivatives
…14: 29.12 Definitions
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15: 29.14 Orthogonality
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29.14.2
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►When combined, all eight systems (29.14.1) and (29.14.4)–(29.14.10) form an orthogonal and complete system with respect to the inner product
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29.14.11
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16: 1.13 Differential Equations
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1.13.4
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17: 28.2 Definitions and Basic Properties
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28.2.2
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18: 27.16 Cryptography
§27.16 Cryptography
… ►For example, a code maker chooses two large primes and of about 400 decimal digits each. Procedures for finding such primes require very little computer time. … ►Choose a prime that does not divide either or . Like , the prime is made public. …19: 23.15 Definitions
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►In §§23.15–23.19, and
denote the Jacobi modulus and complementary modulus, respectively, and () denotes the nome; compare §§20.1 and 22.1.
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►The set of all bilinear transformations of this form is denoted by SL (Serre (1973, p. 77)).
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►If, as a function of , is analytic at , then is called a modular form.
If, in addition, as , then is called a cusp form.
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