유한체 위의 정수론과 기하학

 

메모

• http://www.science.unitn.it/~degraaf/compalg/polfact.pdf
• Michel Waldschmidt Finite fields

 

관련된 항목들

• 유한체 위의 타원곡선에 대한 가우스 정리
• 이차잉여의 상호법칙
• 정수론에서의 상호법칙 (reciprocity laws)
• 체론(field theory)
• 타니야마-시무라 추측(정리)

 

매스매티카 파일 및 계산 리소스

• https://docs.google.com/file/d/0B8XXo8Tve1cxaWJXREZtdmhOdkE/edit

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Factorization_of_polynomials_over_finite_fields

 

강의

• Richard Taylor Primes and Equations, Feb 2012

 

리뷰, 에세이, 강의노트

• Van der Geer, Gerard. “Counting Curves over Finite Fields.” arXiv:1409.6090 [math], September 22, 2014. http://arxiv.org/abs/1409.6090.
• Mazur, Barry. 1993. “On the Passage from Local to Global in Number Theory.” arXiv:math/9307231 (June 30). http://arxiv.org/abs/math/9307231.
• Koblitz, Neal. 1982. Why Study Equations over Finite Fields? Mathematics Magazine 55, no. 3 (May 1): 144-149. doi:10.2307/2690080. 

관련논문

• Narayanan, Anand Kumar. ‘Polynomial Factorization over Finite Fields By Computing Euler-Poincare Characteristics of Drinfeld Modules’. arXiv:1504.07697 [cs, Math], 28 April 2015. http://arxiv.org/abs/1504.07697.
• Achter, Jeffrey D., Daniel Erman, Kiran S. Kedlaya, Melanie Matchett Wood, and David Zureick-Brown. “A Heuristic for the Distribution of Point Counts for Random Curves over a Finite Field.” arXiv:1410.7373 [math], October 27, 2014. http://arxiv.org/abs/1410.7373.