数论及其相关领域

    
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*性能的*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。

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