《数论及其相关领域(英文)》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。

Front Matter
Binary Additive Counter Stream Ciphers
  Cunsheng Ding, Wenpei Si
  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
  Tao Feng, Bin Wen, Qing Xiang, Jianxing Yin
  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 K2OQ(√dp) as p Varies
  Xuejun Guo, Hourong Qin
  1 Introduction
  2 The governing field of the 4-rank of K2OF
  3 The governing field of the 4-rank of K2OF
  References
Word-oriented Linear Feedback Shift Registers: σ-LFSRs
  Wenbao Han, Xianghui Liu, Guang Zeng, Gangmin Tan
  1 Introduction
  2 Modelof σ-LFSR
  3 Cryptographic properties
  4 σ-LFSRs suitable for software implementation
  5 Application of σ-LFSRs
  6 Conclusion
  References
Statistics of Zeros of Families of L-functions over Function Fields:A Survey
  Wen-Ching Winnie Li, Maosheng Xiong
  1 Introduction
  2 Hyperelliptic curves
  3 Cyclic l-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 (?, Γ)-modules
  Yi Ouyang
  1 Introduction
  2 Continuous functions, measures and distributions over Zp
  3 Thep-adic zeta function of Kubota-Leopoldt
  4 (?,Γ)-modules and Galois cohomology
  5 (?,Γ)-modules and Iwasawa theory
  References
Conjectures and Results on x2 mod p2 with 4p = x2 + dy
  Zhi-Wei Sun
  1 Introduction
  2 UsingAp′ery polynomials and products of three binomial
  coefficients
  3 Using the polynomials Sn(x) = nk=0 nk 4xk
  4 Using the function Fn(x) = nk=0 nk 3 2kk x?k
  5 Using the function Gn(x) = nk=0 nk 2 2kk 2n ? 2kn ? k x?k
  6 Usingan(x) = nk=0 nk 2 n + kk xk
  7 Miscellaneous things
  References
Harmonic Weak Maass Forms, Automorphic Green Functions,and Period Integrals
  Tonghai Yang
  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
  Yu Ye, Pu Zhang
  1 Preliminaries
  2 Higher Koszulity
  3 Higher Koszul complexes
  4 Hilbert and Poincar′e series
  5 Dual algebras and Ext-algebras
  6 Generalized d-Koszul modules
  7 Lattice distributivity and Koszulity
  8 More related topics
  References
版权

数学高级讲义ALM

本书不仅是数论及其应用领域专家们的有价值的参考书，也是研究生开展研究时极好的入门书。