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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
- 2001

- Manjul Bhargava
- 2005

- 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)

- Manjul Bhargava
- 2005

This paper is an extended foreword to the paper of Manjul Bhargava [1] in these proceedings, which gives a short and elegant proof of the Conway-Schneeberger Fifteen Theorem on the representation of integers by quadratic forms. The representation theory of quadratic forms has a long history, starting in the seventeenth century with Fermat's assertions of… (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)