Alternate proof of Shô Iseki's functional equation (Q1124968)
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scientific article; zbMATH DE number 1371466
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Alternate proof of Shô Iseki's functional equation |
scientific article; zbMATH DE number 1371466 |
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Alternate proof of Shô Iseki's functional equation (English)
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29 November 1999
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A functional equation derived by \textit{S. Iseki} [Duke Math. J. 24, 653-662 (1957; Zbl 0093.25903)] includes as special cases the transformation theory of the Dedekind modular function \(\eta(\tau)\) and of the reviewer's Lambert series \(G_p(e^{2\pi i\tau})\). Heretofore, the proofs of Iseki's formula relied on complex integration and residue calculus. This paper gives a shorter and simpler proof using Fourier series.
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functional equation
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Dedekind modular function
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Lambert series
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0.9412317
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0.8481896
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0.8465123
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0.8389631
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0.8361294
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0.83511746
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