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

自然科学 数学 代数数论组合理论

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