대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제59권3호
  • /
  • Pages.609-615
  • /
  • 2022
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON THE SIZES OF DUAL GROUPS

  • Song, Joungmin (Division of Liberal Arts & Sciences Gwangju Institute of Science and Technology)
  • 투고 : 2021.01.31
  • 심사 : 2021.12.06
  • 발행 : 2022.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We give a formula for the sizes of the dual groups. It is obtained by generalizing a size estimation of certain algebraic structure that lies in the heart of the proof of the celebrated primality test by Agrawal, Kayal and Saxena. In turn, by using our formula, we are able to give a streamlined survey of the AKS test.

키워드

과제정보

This work was partially supported by 2020 GIST Research Institute and NRF funded by the Ministry of Education, Republic of Korea (2017R1D1A1B0403521).

참고문헌

  1. L. M. Adleman, C. Pomerance, and R. S. Rumely, On distinguishing prime numbers from composite numbers, Ann. of Math. (2) 117 (1983), no. 1, 173-206. https://doi.org/10.2307/2006975
  2. M. Agrawal, N. Kayal, and N. Saxena, PRIMES is in P, Ann. of Math. (2) 160 (2004), no. 2, 781-793. https://doi.org/10.4007/annals.2004.160.781
  3. S. Goldwasser and J. Kilian, Almost all primes can be quickly certified, STOC 86: Proceedings of the eighteenth annual ACM symposium on Theory of computing, 316-329.
  4. S. Lang, Linear Algebra, reprint of the third edition, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1989.
  5. G. L. Miller, Riemann's hypothesis and tests for primality, J. Comput. System Sci. 13 (1976), no. 3, 300-317. https://doi.org/10.1016/S0022-0000(76)80043-8