数论及其相关领域 本书特色
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*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。
数论及其相关领域 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 referencespartial difference sets from quadratic forms and p-ary weakly regular bent functions 1 introduction 2 partial difference sets from quadratic forms and uniformcyclotomy 3 partial difference sets from weakly regular p-ary bentfunctions.. referencesgoverning 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 referencesword-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 referencesstatistics of zeros of families of l-functions over functionfields: a survey 1 introduction 2 hyperelliptic curves 3 cyclic/-fold covers of the projective line 4 elliptic curves over a rational function field andgeneralizations 5 concluding remarks referenceslectures 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 referencesconjectures and results on x2 mod p2 with 4p = x2 + dy2 1 introduction 2 using apery polynomials and products of three binomialcoefficients 3 using the polynomials 4 using the function 5 using the function 6 using 7 miscellaneous things referencesharmonic weak maass forms, automorphic green functions, and periodintegrals 1 introduction 2 shimura varieties of orthogonal type and their kudla cycles 3 harmonic weak maass forms, regularized theta lifting, andautomorphic green functions 4 eisenstein series associated to coherent and incoherentquadratic spaces 5 period integrals of the automorphic green function φ(z, h; f) 6 big cm values of automorphic green functions referencessome 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
