《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 (ϕ, Γ)-modules
- Yi Ouyang
- 1 Introduction
- 2 Continuous functions, measures and distributions over Zp
- 3 Thep-adic zeta function of Kubota-Leopoldt
- 4 (ϕ,Γ)-modules and Galois cohomology
- 5 (ϕ,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
- 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
