Fay trisecant identity
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1: 21.7 Riemann Surfaces
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§21.7(ii) Fay’s Trisecant Identity
… ►For all , and all , , , on , Fay’s identity is given by … ►Generalizations of this identity are given in Fay (1973, Chapter 2). Fay derives (21.7.10) as a special case of a more general class of addition theorems for Riemann theta functions on Riemann surfaces. …2: 21 Multidimensional Theta Functions
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3: 21.1 Special Notation
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►The function is also commonly used; see, for example, Belokolos et al. (1994, §2.5), Dubrovin (1981), and Fay (1973, Chapter 1).
positive integers. | |
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identity matrix. | |
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4: 24.10 Arithmetic Properties
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►where .
…valid when and , where is a fixed integer.
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24.10.8
►valid for fixed integers , and for all such that
and .
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24.10.9
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5: Bibliography F
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Theta Functions on Riemann Surfaces.
Springer-Verlag, Berlin.
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6: 27.16 Cryptography
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►Thus, and .
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►By the Euler–Fermat theorem (27.2.8), ; hence .
But , so is the same as modulo .
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7: 36.9 Integral Identities
8: 26.21 Tables
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►Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts , partitions into parts , and unrestricted plane partitions up to 100.
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