#### Filter Results:

- Full text PDF available (26)

#### Publication Year

1997

2015

- This year (0)
- Last 5 years (14)
- Last 10 years (20)

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- Manjul Bhargava
- The American Mathematical Monthly
- 2000

Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Each copy of any part of a JSTOR transmission must contain the same copyright notice that… (More)

- MANJUL BHARGAVA
- 2009

Contents 1. Introduction 963 2. A game called í µí±-orderings 967 2.1. On í µí±-removed í µí±-orderings 968 2.2. On í µí±-orderings of order ℎ 969 3. Rings of integer-valued polynomials 969 3.1. Polynomials with integer-valued divided differences 970 3.2. Integer-valued polynomials having a given modulus 973 4. Smooth functions on compact subsets of… (More)

We prove that when all hyperelliptic curves of genus n ≥ 1 having a rational Weierstrass point are ordered by height, the average size of the 2-Selmer group of their Jacobians is equal to 3. It follows that (the limsup of) the average rank of the Mordell-Weil group of their Jacobians is at most 3/2. The method of Chabauty can then be used to obtain an… (More)

Using only linear algebra over Z p , we dene a discrete probability distribution on the set of isomorphism classes of short exact sequences of Z p-modules, and then conjecture that as E varies over elliptic curves over a xed global eld k, the distribution of is that one. This single conjecture would explain many of the known theorems and conjectures on… (More)