q-series, elliptic curves, and odd values of the partition function
Let p(n) be the number of partitions of an integer n. Euler proved the following recurrence for p(n): p(n)=∑k=1∞(−1)k+1(p(n−ω(k))+p(n−ω(−k))), (*) where ω(k)=(3k 2+k)/2. In view of Euler's result, one sees that it is fairly easy to compute p(n) very quickl...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171299220558 |
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