Now showing items 1-20 of 25

• #### About Hermann Weyl’s “Ramifications, Old and New, of the Eigenvalue Problem” ﻿

(American Mathematical Society (AMS), 2012-05-01)
• #### Arithmetic on Curves ﻿

(American Mathematical Society (AMS), 1986-04-01)
• #### Average Ranks of Elliptic Curves: Tension between Data and Conjecture ﻿

(American Mathematical Society, 2007)
Rational points on elliptic curves are the gems of arithmetic: they are, to diophantine geometry, what units in rings of integers are to algebraic number theory, what algebraic cycles are to algebraic geometry. A rational ...
• #### A celebration of the mathematical work of Glenn Stevens ﻿

(Springer Nature, 2015)
• #### Complete Homogeneous Varieties via Representation Theory ﻿

(2016-05-02)
Given an algebraic variety $X\subset\PP^N$ with stabilizer $H$, the quotient $PGL_{N+1}/H$ can be interpreted a parameter space for all $PGL_{N+1}$-translates of $X$. We define $X$ to be a \textit{homogeneous variety} if ...
• #### Computation of p-Adic Heights and Log Convergence ﻿

(Universität Bielefeld, Fakultät für Mathematik, 2006)
This paper is about computational and theoretical questions regarding p-adic height pairings on elliptic curves over a global field K. The main stumbling block to computing them efficiently is in calculating, for each of ...
• #### Correspondence Homomorphisms for Singular Varieties ﻿

(Cellule MathDoc/CEDRAM, 1994)
We study certain kinds of geometric correspondences between (possibly singular) algebraic varieties and we obtain comparison results regarding natural filtrations on the homology of varieties.
• #### Disparity in Selmer Ranks of Quadratic Twists of Elliptic Curves ﻿

(Princeton University, Department of Mathematics, 2013)
We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We prove that the fraction of twists (of a given elliptic curve over a fixed number ...
• #### Finding Large Selmer Rank via an Arithmetic Theory of Local Constants ﻿

(Princeton University, 2007)
We obtain lower bounds for Selmer ranks of elliptic curves over dihedral extensions of number fields. Suppose $K∕k$ is a quadratic extension of number fields, $E$ is an elliptic curve defined over k,and p is an odd ...
• #### Finding Meaning in Error Terms ﻿

(American Mathematical Society (AMS), 2008-02-06)
• #### Growth of Selmer Rank in Nonabelian Extensions of Number Fields ﻿

(Duke University Press, 2008)
Let $p$ be an odd prime number, let E be an elliptic curve over a number field $k$, and let $F/k$ be a Galois extension of degree twice a power of p. We study the $Z_p$-corank $rk_p(E/F)$ of the $p$-power Selmer ...
• #### Mathematical Platonism and its Opposites ﻿

(European Mathematical Society, 2008)
• #### Mathematics: Controlling Our Errors ﻿

(Nature Publishing Group, 2006)
The Sato–Tate conjecture holds that the error term occurring in many important problems in number theory conforms to a specific probability distribution. That conjecture has now been proved for a large group of cases. Even ...
• #### Nearly Ordinary Galois Deformations over Arbitrary Number Fields ﻿

(Cambridge University Press, 2009)
Let $K$ be an arbitrary number field, and let $\rho: Gal(K \bar/K) \rightarrow GL_2(E)$ be a nearly ordinary irreducible geometric Galois representation. In this paper, we study the nearly ordinary deformations of ...
• #### On Mathematics, Imagination and the Beauty of Numbers ﻿

(Massachusetts Institute of Technology Press, 2005)
• #### On the Passage From Local to Global in Number Theory ﻿

(American Mathematical Society (AMS), 1993-07-01)
• #### Organizing the Arithmetic of Elliptic Curves ﻿

(Elsevier BV, 2005-12)
Suppose that E is an elliptic curve defined over a number field K, p is a rational prime, and K-infinity is the maximal Z(p)-power extension of K. In previous work [B. Mazur, K. Rubin, Elliptic curves and class field theory, ...
• #### Perturbations, Deformations, and Variations (and "Near-Misses") in Geometry, Physics, and Number Theory ﻿

(American Mathematical Society, 2004)
• #### Pourquoi les Nombres Premiers? ﻿

(La Recherche, 2005)
À l’image des atomes pour les molécules, les nombres premiers sont les briques élémentaires des nombres entiers. Quantité de problèmes sur les premiers sont aussi simples à énoncer que difficiles à attaquer. Un éminent ...
• #### Ranks of Twists of Elliptic Curves and Hilbert’s Tenth Problem ﻿

(Springer Verlag, 2010)
In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer ...