Gauss sum
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1: 27.10 Periodic Number-Theoretic Functions
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►Another generalization of Ramanujan’s sum is the Gauss sum
associated with a Dirichlet character .
…In particular, .
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is separable for some if
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►For a primitive character , is separable for every , and
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►Conversely, if is separable for every , then is primitive (mod ).
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2: 20.11 Generalizations and Analogs
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§20.11(i) Gauss Sum
►For relatively prime integers with and even, the Gauss sum is defined by ►
20.11.1
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20.11.2
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3: 5.16 Sums
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►For related sums involving finite field analogs of the gamma and beta functions (Gauss and Jacobi sums) see Andrews et al. (1999, Chapter 1) and Terras (1999, pp. 90, 149).
4: 17.7 Special Cases of Higher Functions
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-Analog of Bailey’s Sum
… ►-Analog of Gauss’s Sum
… ►-Analog of Dixon’s Sum
… ►Gasper–Rahman -Analog of Watson’s Sum
… ►Gasper–Rahman -Analog of Whipple’s Sum
…5: 17.6 Function
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-Gauss Sum
…6: 16.4 Argument Unity
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16.4.2_5
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7: 18.38 Mathematical Applications
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18.38.3
, , ,
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8: 34.2 Definition: Symbol
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►where is defined as in §16.2.
►For alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§8.21, 8.24–8.26).
9: 34.4 Definition: Symbol
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►For alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§9.2.1, 9.2.3).