This paper gives an improved lower bound on the degrees d such that for general points p 1 p n β P 2 and m > 0 there is a plane curve of degree d vanishing at each p i with multiplicity at least m.
On Kummer's Conjecture
β Scribed by M.Ram Murty; Yiannis N Petridis
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 120 KB
- Volume
- 90
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
β¦ Synopsis
Kummer conjectured the asymptotic behavior of the first factor of the class number of a cyclotomic field. If we only ask for upper and lower bounds of the order of growth predicted by Kummer, then this modified Kummer conjecture is true for almost all primes.
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