內容簡介
《數論及其相關領域(英文)》內容定位於馮克勤教授作出重要成就及感興趣的領域，分為兩個方面：一方面是數論，包括二次丟番圖方程的同餘性、代數整數環的K群、整體函式域的L-函式、自守形式以及p-adic表示等，另一方面是這些理論在設計、編碼等領域的套用，反映了馮克勤教授在數論及其套用領域的發展所作的貢獻和影響。
圖書目錄
BinaryAdditiveCounterStreamCiphers
1Introduction
2Possibleattacksanddesigncriteria
3Example1:theLegendrecipher
4Example2:thetwo-primecipher
5Conclusionsandconcludingremarks
References
PartialDifferenceSetsfromQuadraticFormsandp-aryWeakly
RegularBentFunctions
1Introduction
2Partialdifferencesetsfromquadraticformsanduniformcyclotomy
3Partialdifferencesetsfromweaklyregularp-arybentfunctions..
References
GoverningFieldsofthe4-rankofK20o~./~aspVaries
1Introduction
2Thegoverningfieldofthe4-rankofK20F
3Thegoverningfieldofthe8-rankofK20F
References
Word-orientedLinearFeedbackShiftRegisters:a-LFSRs
1Introduction
2Modelofa-LFSR
3Cryptographicproperties
4a-LFSRssuitableforsoftwareimplementation
5Applicationofa-LFSRs
6Conclusion
References
StatisticsofZerosofFamiliesofL-functionsoverFunctionFields:ASurvey
1Introduction
2Hyperellipticcurves
3Cyclic/-foldcoversoftheprojectiveline
4Ellipticcurvesoverarationalfunctionfieldandgeneralizations
5Concludingremarks
References
Lecturesonp-adicZetaFunctionsand(ч,г)-modules
1Introduction
2Continuousfunctions,measuresanddistributionsoverZp
3Thep-adiczetafunctionofKubota-Leopoldt
4(ч,г)-modulesandGaloiscohomology
5(ч,г)-modulesandIwasawatheory
References
ConjecturesandResultsonx2modp2with4p=x2+dy2
1Introduction
2UsingAperypolynomialsandproductsofthreebinomialcoefficients
3Usingthepolynomials
4Usingthefunction
5Usingthefunction
6Using
7Miscellaneousthings
References
HarmonicWeakMaassForms,AutomorphicGreenFunctions,andPeriodIntegrals
1Introduction
2ShimuravarietiesoforthogonaltypeandtheirKudlacycles
3HarmonicweakMaassforms,regularizedthetalifting,andautomorphicGreenfunctions
4Eisensteinseriesassociatedtocoherentandincoherentquadraticspaces
5PeriodintegralsoftheautomorphicGreenfunctionφ(z,h;f)
6BigCMvaluesofautomorphicGreenfunctions
References
SomeRecentProgressinHigherKoszulity
1Preliminaries
2HigherKoszulity
3HigherKoszulcomplexes
4HilbertandPoincareseries
5DualalgebrasandExt-algebras
6Generalizedd-Koszulmodules
7LatticedistributivityandKoszulity
8Morerelatedtopics
References
