Small zeros of quadratic forms modulo p
โ Scribed by Todd Cochrane
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 276 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We use a telescoping method suggested by Ono [5] to compute p(n) (mod l) as a weighted sum over l-affine partitions of size n. When l=2, 3, 5, 7, and 11, these sums are neatly described using binary quadratic forms. Moreover, one immediately obtains classical proofs of the Ramanujan congruences (mod
Let N be the number of affine zeros of a pair of quadratic forms in n#1 variables defined over a finite field F O . We give upper and lower bounds for N and show that these bounds are optimal. One result states that if n#1510 and every quadratic form in the pencil has order at least three, then "N!q