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On the Surjectivity of Galois Representations Associated to Elliptic Curves over Number Fields
Surjectivity Galois Representations Elliptic Curves over Number Fields Number Theory
2012/4/17
Given an elliptic curve $E$ over a number field $K$, the $\ell$-torsion points $E[\ell]$ of $E$ define a Galois representation $\gal(\bar{K}/K) \to \gl_2(\ff_\ell)$. A famous theorem of Serre states t...
Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
Pairing-based algorithms jacobians of genus 2 curves maximal endomorphism ring Number Theory
2012/4/17
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the $\ell$-Tate pairing in terms of the action of the Frobenius on the $\ell$-torsion of the Jacobian of a ge...
An ordinary cyclotomic function field
ordinary cyclotomic function field investigate $p$-rank
2012/3/1
In this paper, we investigate the $p$-rank of Jacobian of cyclotomic function field $K_m$. Our goal in this paper is to give the necessary and sufficient condition $m$ such that $K_m$ is ordinary.
Given a finite set $S$ of places of a number field, we prove that the field of totally $S$-adic algebraic numbers is not Hilbertian.
We prove a refinement of the results of Gross and Zagier on prime factorizations of singular moduli.
Intersection theory on Shimura surfaces II
Intersection theory Shimura surfaces II Number Theory
2012/3/1
This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed t...
Deforming endomorphisms of supersingular Barsotti-Tate groups
Deforming endomorphisms supersingular Barsotti-Tate groups Number Theory
2012/3/1
The formal deformation space of a supersingular Barsotti-Tate group over of dimension two equipped with an action of Z_{p^2} is known to be isomorphic to the formal spectrum of a power series ring in ...
Intersection theory on Shimura surfaces
Intersection theory Shimura surfaces intersection multiplicities
2012/3/1
Kudla has proposed a general program to relate arithmetic intersection multiplicities of special cycles on Shimura varieties to Fourier coefficients of Eisenstein series. The lowest dimensional case, ...
A universal first order formula defining the ring of integers in a number field
universal first order formula defining ring integers number field
2012/3/1
We show that the complement of the ring of integers in a number field K is Diophantine. This means the set of ring of integers in K can be written as {t in K | for all x_1, ..., x_N in K, f(t,x_1, ......
The theorems of Gross-Zagier and Zhang relate the N\'eron-Tate heights of complex multiplication points on the modular curve X_0(N) (and on Shimura curve analogues) with the central derivatives of aut...
Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems
ExpectedStochastic CombinatorialProblems
2012/12/4
We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest ...
We give an explicit construction of a pseudorandom generator for read-once formulas whose inputs can be read in arbitrary order. For formulas in n inputs and arbitrary gates of fan-in at most d = O(n=...
Computationally Limited Randomness
randomness, limited randomness, probabilistic polynomial time, hierarchy, stack machine.
2012/12/3
The starting point of this work is the basic question of whether there exists a formal and meaningful way to limit the computational power that a time bounded randomized Turing Machine can employ on i...
Goldbach问题的三种解决方案
分割筛法 整数分类筛法 轻筛法 Goldbach问题 孪生素数问题
2011/9/22
术语“命题 {1, b}”指每一个大偶数N都可以表为一个素数与一个不超过b个素因子的乘积之和. Goldbach问题中的筛法总是要求筛除每一个合数，这一要求通常会给筛法本身带来巨大的麻烦. 其实这个要求是不必要的. 作者发现，在仅仅筛除部分合数的情况下，至少存在3种方法可以解决Goldbach问题. 第一种方法是分割筛法. 其实在任意命题 {1, b} 得到证明的同时也就证明了命题 {1, 1}....