フォン・マンゴルト関数のフーリエ変換は、リーマンゼータ関数の零点の虚数部に等しい座標にスパイクのあるスペクトルを与える。これは、二重性と呼ばれることがある。
関連項目
脚注
- ^ Apostol (1976) p.32
- ^ a b Tenenbaum (1995) p.30
- ^ Apostol (1976) p.33
- ^ Schroeder, Manfred R. (1997). Number theory in science and communication. With applications in cryptography, physics, digital information, computing, and self-similarity. Springer Series in Information Sciences. 7 (3rd ed.). Berlin: Springer-Verlag. ISBN 3-540-62006-0. Zbl 0997.11501
- ^ Hardy & Wright (2008) §17.7, Theorem 294
- ^ Apostol (1976) p.246
- ^ Hardy, G. H.; Littlewood, J. E. (1916). “Contributions to the Theory of the Riemann Zeta-Function and the Theory of the Distribution of Primes”. Acta Mathematica 41: 119–196. doi:10.1007/BF02422942 2014年7月3日閲覧。.
- ^ Conrey, J. Brian (March 2003). “The Riemann hypothesis”. Notices Am. Math. Soc. 50 (3): 341–353. Page 346
- Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag, ISBN 978-0-387-90163-3, MR0434929, Zbl 0335.10001
- Hardy, G. H.; Wright, E. M. (2008) [1938]. Heath-Brown, D. R.; Silverman, J. H.. eds. An Introduction to the Theory of Numbers (6th ed.). Oxford: Oxford University Press. ISBN 978-0-19-921985-8. MR2445243. Zbl 1159.11001
- Tenebaum, Gérald C.B. Thomas訳 (1995). Introduction to analytic and probabilistic number theory. Cambridge Studies in Advanced Mathematics. 46. Cambridge: Cambridge University Press. ISBN 0-521-41261-7. Zbl 0831.11001
外部リンク
- Allan Gut, Some remarks on the Riemann zeta distribution (2005)
- S.A. Stepanov (2001), “Mangoldt function”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- Chris King, Primes out of thin air (2010)
- Heike, How plot Riemann zeta zero spectrum in Mathematica? (2012)
