数论及其相关领域（英文版）
作者：欧阳毅 主编
出版时间：2013年版
内容简介
冯克勤教授师从华罗庚先生，专攻数论方向，他将数论用于代数编码理论和代数图论，首次引进了“因子关联图”的概念，并对其特性进行深入研究；利用这一工具，对于有保密通信背景的M序列反馈逻辑的构作予以重大推进。另外，他利用Weil和这一深刻的数论工具得到线性移存器序列伪随机性能的最佳结果；同时，还得到以表示论为背景的Ramanujan超图的谱性。近年来，他对具有密码学性质的布尔函数研究受到国内外的极大关注。《数论及其相关领域》内容定位于冯克勤教授作出重要成就及感兴趣的领域，分为两个方面：一方面是数论，包括二次丢番图方程的同余性、代数整数环的K群、整体函数域的L-函数、自守形式以及p-adic表示等，另一方面是这些理论在设计、编码等领域的应用，反映了冯克勤教授在数论及其应用领域的发展所作的贡献和影响，《数论及其相关领域》不仅是数论及其应用领域专家们有价值的参考书，也是研究生开展研究时极好的入门书。本书由欧阳毅等主编。
目录
Binary Additive Counter Stream Ciphers 1 Introduction 2 Possible attacks and design criteria 3 Example 1: the Legendre cipher 4 Example 2: the two-prime cipher 5 Conclusions and concluding remarks References Partial Difference Sets from Quadratic Forms and p-ary Weakly Regular Bent Functions 1 Introduction 2 Partial difference sets from quadratic forms and uniform cyclotomy 3 Partial difference sets from weakly regular p-ary bent functions.. References Governing Fields of the 4-rank of K20o~./~ as p Varies 1 Introduction 2 The governing field of the 4-rank of K20F 3 The governing field of the 8-rank of K20F References Word-oriented Linear Feedback Shift Registers: a-LFSRs 1 Introduction 2 Model of a-LFSR 3 Cryptographic properties 4 a-LFSRs suitable for software implementation 5 Application of a-LFSRs 6 Conclusion References Statistics of Zeros of Families of L-functions over Function Fields: A Survey 1 Introduction 2 Hyperelliptic curves 3 Cyclic/-fold covers of the projective line 4 Elliptic curves over a rational function field and generalizations 5 Concluding remarks References Lectures on p-adic Zeta Functions and (ч, г)-modules 1 Introduction 2 Continuous functions, measures and distributions over Zp 3 The p-adic zeta function of Kubota-Leopoldt 4 (ч, г)-modules and Galois cohomology 5 (ч,г)-modules and Iwasawa theory References Conjectures and Results on x2 mod p2 with 4p = x2 + dy2 1 Introduction 2 Using Apery polynomials and products of three binomial coefficients 3 Using the polynomials 4 Using the function 5 Using the function 6 Using 7 Miscellaneous things References Harmonic Weak Maass Forms, Automorphic Green Functions, and Period Integrals 1 Introduction 2 Shimura varieties of orthogonal type and their Kudla cycles 3 Harmonic weak Maass forms, regularized theta lifting, and automorphic Green functions 4 Eisenstein series associated to coherent and incoherent quadratic spaces 5 Period integrals of the automorphic Green function φ(z, h; f) 6 Big CM values of automorphic Green functions References Some Recent Progress in Higher Koszulity 1 Preliminaries 2 Higher Koszulity 3 Higher Koszul complexes 4 Hilbert and Poincare series 5 Dual algebras and Ext-algebras 6 Generalized d-Koszul modules 7 Lattice distributivity and Koszulity 8 More related topics References
