Some new old-fashioned modular identities (Q1265270)
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scientific article; zbMATH DE number 1203266
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some new old-fashioned modular identities |
scientific article; zbMATH DE number 1203266 |
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Some new old-fashioned modular identities (English)
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8 April 1999
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The paper uses modular functions on the theta group to derive an exact formula for the sum \[ \sum_{| j|\leq\sqrt u}\sigma(u-j^2) \] in terms of the singular series for the number of representations of an integer as a sum of 5 squares (here \(\sigma(k)\) denotes the sum of the divisors of \(k\) if \(k\) is a positive integer and \(\sigma(0) =-{1\over 24})\). Several related identities are derived and discussed.
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modular identities
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sums of squares
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sum of divisors
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modular functions
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theta group
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