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On the Circular Summation of the Eleventh Powers of Ramanujan's Theta Function

✍ Scribed by Ken Ono

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 94 KB
Volume: 76
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2354

No coin nor oath required. For personal study only.

✦ Synopsis

Let f (a, b) denote Ramanujan's theta series. In his Lost Notebook'', Ramanujan claimed that the circular'' summation of n th powers of f satisfies a factorization of the form f (a n , b n ) F n (a n b n ) where F n (q)=1+2nq (n&1)Â2 + } } } . Moreover, he listed explicit closed formulas for F 2 , F 3 , F 4 , F 5 , and F 7 . Berndt and Son have asked for a similar expression for any other F n . Here we obtain such an expression for F 11 (q).

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