Zobrazeno 1 - 10
of 11
pro vyhledávání: '"Hiroki SUMIDA-TAKAHASHI"'
Publikováno v:
Journal of the Mathematical Society of Japan. 74(3):945-972
Let p be an odd prime number and let 2e+1 be the highest power of 2 dividing p − 1. For 0 ≤ n ≤ e, let kn be the real cyclic field of conductor p and degree 2n. For a certain imaginary quadratic field L0, we put Ln = L0kn. For 0 ≤ n ≤ e −
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::93c6d884751210db29b255ce22b802d4
http://repo.lib.tokushima-u.ac.jp/117035
http://repo.lib.tokushima-u.ac.jp/117035
Autor:
Hiroki Sumida-Takahashi
Publikováno v:
Arnold Mathematical Journal.
In order to discuss the validity of the Kummer-Vandiver conjecture, we consider a generalized problem associated to the conjecture. Let p be an odd prime number and ζp a primitive p-th root of unity. Using new programs, we compute the Iwasawa invari
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::61e1b01b8ed71b451a03e8a8c1cc752a
https://doi.org/10.1007/s40598-022-00220-3
https://doi.org/10.1007/s40598-022-00220-3
Publikováno v:
Tokyo Journal of Mathematics. 44(1):157-173
Let $p=2^{e+1}q+1$ be an odd prime number with $2 \nmid q$. Let $K$ be the imaginary cyclic field of conductor $p$ and degree $2^{e+1}$. We denote by $\mathcal{F}$ the imaginary quadratic subextension of the imaginary $(2,\,2)$-extension $K(\sqrt{2})
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ba897a98d163d3aebaaaac14e22852ea
http://repo.lib.tokushima-u.ac.jp/115612
http://repo.lib.tokushima-u.ac.jp/115612
Publikováno v:
Journal de Théorie des Nombres de Bordeaux. 28:325-345
Let ℓ be an odd prime number. Let K/Q be a real cyclic extension of degree ℓ, AK the 2-part of the ideal class group of K, and H/K the class field corresponding to AK/A2K. Let Kn be the nth layer of the cyclotomic Z2-extension over K. We consider
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f6c72ee2ff52ede4639652f83336696
https://doi.org/10.5802/jtnb.942
https://doi.org/10.5802/jtnb.942
Publikováno v:
International Journal of Number Theory. 10:283-296
Let p be an odd prime number, Kn = Q(ζpn+1) the pn+1th cyclotomic field and [Formula: see text] the relative class number of Kn. Fixing an integer d ∈ Z with [Formula: see text], we denote by Ln the imaginary quadratic subextension of the imaginar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bb81916744e62f9b5e20e36e7f94a562
https://doi.org/10.1142/s1793042113500929
https://doi.org/10.1142/s1793042113500929
Publikováno v:
Journal of Number Theory. 133:787-801
Let p be an odd prime number with p≠3, and K=Q(cos(2π/p),ζ3). Let Kn be the n-th layer of the cyclotomic Zp-extension over K, and λn the Iwasawa lambda invariant of the cyclotomic Z3-extension over Kn. By a theorem of Friedman, it is known that
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::84acc46686ba235c165a2e9b07aa485f
https://doi.org/10.1016/j.jnt.2012.08.022
https://doi.org/10.1016/j.jnt.2012.08.022
Publikováno v:
Acta Arithmetica. 136:385-389
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6d0db500b4d887c8d1aeb88ac6f218d9
https://doi.org/10.4064/aa136-4-5
https://doi.org/10.4064/aa136-4-5
Autor:
Hiroki Sumida-Takahashi
Publikováno v:
Mathematics of Computation. 76:1059-1071
Under Greenberg's conjecture, we give an efficient method to compute the p-part of the ideal class group of certain real abelian fields by using cyclotomic units, Gauss sums and prime numbers. As numerical examples, we compute the p-part of the ideal
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c8d66554bc0a2934290b7179367c5ecb
https://doi.org/10.1090/s0025-5718-07-01926-6
https://doi.org/10.1090/s0025-5718-07-01926-6
Publikováno v:
Acta Arithmetica. 127:179-191
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8d68bc407d6fcd1474113621844b37c6
https://doi.org/10.4064/aa127-2-7
https://doi.org/10.4064/aa127-2-7
Autor:
Hiroki Sumida-Takahashi
Publikováno v:
Experimental Mathematics. 14:307-316
Using fast algorithms, we compute the Iwasawa invariants of Q( √ f, ζp) in the range 1
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::45a4df5fe5ace195a85cf1292e4faa09
https://doi.org/10.1080/10586458.2005.10128926
https://doi.org/10.1080/10586458.2005.10128926