関連論文
-
On the analytic behaviour of higher derivatives of Hardy's Z-function, and a certain discrete moment of the first derivative of Dirichlet L-functions
-
Mathematical Studies on Quantum Systems and Locally Quantum Systems
-
Embedding optimization problems for a graph related to Laplacian eigenvalue maximization
-
内臓脂肪組織内の時計遺伝子Dbpの発現変動に伴うインスリン感受性への影響
-
Cluster categories of formal dg algebras and hereditary Calabi-Yau categories
参考文献
[1] Scot Adams and Peter Sarnak, Betti numbers of congruence groups With an appendix
by Ze’ev Rudnick, Israel J. Math., 88 (1994), no. 1-3, 31–72.
[2] Tom M. Apostol, Resultants of cyclotomic polynomials, Proc. Amer. Math. Soc. 24
(1970), 457–462.
[3] David Cimasoni, Studying the multivariable Alexander polynomial by means of Seifert
surfaces, Bol. Soc. Mat. Mexicana (3) 10 (2004), Special Issue, 107–115.
[4] Albert A. Cuoco and Paul Monsky, Class numbers in Zdp -extensions, Math. Ann. 255
(1981), no. 2, 235–258.
[5] Sage DuBose and Daniel Valli`eres, On Zdl -towers of graphs, preprint. arXiv:2207.01711
[6] Jonathan Hillman, Algebraic invariants of links. Second edition, Series on Knots and
Everything, 52. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012.
[7] Jonathan Hillman, Daniel Matei, and Masanori Morishita, Pro-p link groups and phomology groups, Primes and knots, 121–136, Contemp. Math., 416, Amer. Math. Soc.,
Providence, RI, 2006.
[8] Richard Hartley, The Conway potential function for links, Comment. Math. Helv. 58
(1983), no. 3, 365–378.
[9] Eriko Hironaka, Polynomial periodicity for Betti numbers of covering surfaces, Invent.
Math., 108 (1992), no. 2, 289–321.
[10] Kenkichi Iwasawa, On Γ-extensions of algebraic number fields, Bull. Amer. Math. Soc.,
65 (1959), 183–226.
[11] Kenkichi Iwasawa, On the µ-invariants of Zl -extensions, in: Number Theory, Algebraic
Geometry and Commutative Algebra, in Honor of Yasuo Akizuki, Kinokuniya, Tokyo,
1973, pp. 1–11.
[12] Uwe Jannsen, Continuous ´etale cohomology, Math. Ann. 280 (1988), no. 2, 207–245.
[13] Teruhisa Kadokami and Yasushi Mizusawa, Iwasawa type formula for covers of a link in
a rational homology sphere, J. Knot Theory Ramifications, 17 (2008), no. 10, 1199–1221.
36
[14] Mark E. Kidwell, Alexander polynomials of links of small order, Illinois J. Math. 22
(1978), no. 3, 459–475.
[15] Steffen Kionke, On p-adic limits of topological invariants, J. Lond. Math. Soc. (2) 102
(2020), no. 2, 498–534.
[16] Hershy Kisilevsky, A generalization of a result of Sinnott, Olga Taussky-Todd: in memoriam. Pacific J. Math. 1997, Special Issue, 225–229.
[17] Paul Monsky, On p-adic power series, Math. Ann., 255 (1981), no. 2, 217–227.
[18] Paul Monsky, Fine estimates for the growth of en in Zdp -extensions, Algebraic number
theory, 309–330, Adv. Stud. Pure Math., 17, Academic Press, Boston, MA, 1989.
[19] Masanori Morishita, Knots and primes, An introduction to arithmetic topology. Universitext. Springer, London, 2012.
[20] Douglas Geoffrey Northcott, Finite free resolutions, Cambridge Tracts in Mathematics,
No. 71. Cambridge University Press, Cambridge-New York-Melbourne, 1976. xii+271
pp.
[21] Tadashi Ochiai, Iwasawa theory and its perspective I, Iwanami Studies in Advanced
Mathematics (2014).
[22] Manabu Ozaki, Construction of Zp -extensions with prescribed Iwasawa modules, J.
Math. Soc. Japan, 56 (2004), no. 3, 787–801.
[23] Joan Porti, Mayberry-Murasugi’s formula for links in homology 3-spheres, Proc. Amer.
Math. Soc., 132 (2004), no. 11, 3423–3431.
[24] Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7. Publish or Perish,
Inc., Berkeley, Calif., 1976.
[25] The Sage Developers, SageMath, the Sage Mathematics Software System (Version 9.7),
https://www.sagemath.org, 2023.
[26] Makoto Sakuma, Homology of abelian coverings of links and spatial graphs, Canad. J.
Math., 47 (1995), no. 1, 201–224.
[27] Romyar Sharifi, Iwasawa theory. https://www.math.ucla.edu/~sharifi/iwasawa.
[28] Sohei Tateno and Jun Ueki, The Iwasawa invariants of Zdp -covers of links, in preparation.
[29] Jun Ueki, On the homology of branched coverings of 3-manifolds, Nagoya Math. J. 213
(2014), 21–39.
37
[30] Jun Ueki, On the Iwasawa µ-invariants of branched Zp -covers, Proc. Japan Acad. Ser.
A Math. Sci., 92 (2016), no. 6, 67–72.
[31] Jun Ueki, On the Iwasawa invariants for links and Kida’s formula, Internat. J. Math.
28 (2017), no. 6, 1750035, 30 pp.
[32] Jun Ueki and Hyuga Yoshizaki, The p-adic limits of class numbers in Zp -towers,
preprint. arXiv:2210.06182
[33] Daqing Wan, Class numbers and p-ranks in Zdp -towers, J. Number Theory, 203 (2019),
139–154.
[34] Lawrence C. Washington, Introduction to Cyclotomic Fields, second ed., Graduate Texts
in Mathematics, vol. 83, Springer-Verlag, New York, 1997.
Sohei Tateno
Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya, 4648602, Japan
E-mail address: inu.kaimashita@gmail.com
38
...