Ichimura, Humio Relative class numbers inside the \(p\)th cyclotomic field. (English) Zbl 07285619 Osaka J. Math. 57, No. 4, 949-959 (2020). Reviewer: Antonio M. Oller Marcén (Zaragoza) MSC: 11R29 11R18 PDF BibTeX XML Cite \textit{H. Ichimura}, Osaka J. Math. 57, No. 4, 949--959 (2020; Zbl 07285619) Full Text: Euclid
Burungale, Ashay; Sun, Hae-Sang Quantitative non-vanishing of Dirichlet \(L\)-values modulo \(p\). (English) Zbl 07250829 Math. Ann. 378, No. 1-2, 317-358 (2020). MSC: 11R18 11R29 11R42 11R23 PDF BibTeX XML Cite \textit{A. Burungale} and \textit{H.-S. Sun}, Math. Ann. 378, No. 1--2, 317--358 (2020; Zbl 07250829) Full Text: DOI
Ohta, Masami \( \mu \)-type subgroups of \(J_1(N)\) and application to cyclotomic fields. (English) Zbl 07196907 J. Math. Soc. Japan 72, No. 2, 333-412 (2020). MSC: 11G18 14G05 11R23 PDF BibTeX XML Cite \textit{M. Ohta}, J. Math. Soc. Japan 72, No. 2, 333--412 (2020; Zbl 07196907) Full Text: DOI Euclid
Morisawa, Takayuki; Okazaki, Ryotaro Height and Weber’s class number problem. (English. French summary) Zbl 1415.11165 J. Théor. Nombres Bordx. 28, No. 3, 811-828 (2016). MSC: 11R29 11R18 PDF BibTeX XML Cite \textit{T. Morisawa} and \textit{R. Okazaki}, J. Théor. Nombres Bordx. 28, No. 3, 811--828 (2016; Zbl 1415.11165) Full Text: DOI
Burungale, Ashay A. An \(l\neq p\)-interpolation of genuine \(p\)-adic \(L\)-functions. (English) Zbl 1398.11075 Res. Math. Sci. 3, Paper No. 16, 26 p. (2016). MSC: 11F33 11F41 11G18 11R23 PDF BibTeX XML Cite \textit{A. A. Burungale}, Res. Math. Sci. 3, Paper No. 16, 26 p. (2016; Zbl 1398.11075) Full Text: DOI
Fujima, Shoichi; Ichimura, Humio Note on the class number of the \(p\)th cyclotomic field. (English) Zbl 1388.11076 Funct. Approximatio, Comment. Math. 52, No. 2, 299-309 (2015). MSC: 11R29 11R18 PDF BibTeX XML Cite \textit{S. Fujima} and \textit{H. Ichimura}, Funct. Approximatio, Comment. Math. 52, No. 2, 299--309 (2015; Zbl 1388.11076) Full Text: DOI Euclid
Dokchitser, Tim; Dokchitser, Vladimir Growth of \({\text Ш}\) in towers for isogenous curves. (English) Zbl 1351.11035 Compos. Math. 151, No. 11, 1981-2005 (2015). Reviewer: Andrea Bandini (Parma) MSC: 11G10 11G40 11G05 11G07 11R23 11D68 PDF BibTeX XML Cite \textit{T. Dokchitser} and \textit{V. Dokchitser}, Compos. Math. 151, No. 11, 1981--2005 (2015; Zbl 1351.11035) Full Text: DOI arXiv
Lamplugh, J. An analogue of the Washington-Sinnott theorem for elliptic curves with complex multiplication. I. (English) Zbl 1323.11035 J. Lond. Math. Soc., II. Ser. 91, No. 3, 609-642 (2015). Reviewer: Lawrence C. Washington (College Park) MSC: 11G05 11R23 11G40 11G15 11R29 PDF BibTeX XML Cite \textit{J. Lamplugh}, J. Lond. Math. Soc., II. Ser. 91, No. 3, 609--642 (2015; Zbl 1323.11035) Full Text: DOI
Miller, John C. Class numbers in cyclotomic \(\mathbb{Z}_p\)-extensions. (English) Zbl 1319.11078 J. Number Theory 150, 47-73 (2015). Reviewer: Günter Lettl (Graz) MSC: 11R29 11R23 11Y40 PDF BibTeX XML Cite \textit{J. C. Miller}, J. Number Theory 150, 47--73 (2015; Zbl 1319.11078) Full Text: DOI
Klagsbrun, Zev; Lemke Oliver, Robert J. The distribution of the Tamagawa ratio in the family of elliptic curves with a two-torsion point. (English) Zbl 1349.11094 Res. Math. Sci. 1, Paper No. 15, 10 p. (2014). MSC: 11G05 14H52 14H25 PDF BibTeX XML Cite \textit{Z. Klagsbrun} and \textit{R. J. Lemke Oliver}, Res. Math. Sci. 1, Paper No. 15, 10 p. (2014; Zbl 1349.11094) Full Text: DOI arXiv
Fukuda, Takashi; Komatsu, Keiichi; Morisawa, Takayuki Weber’s class number one problem. (English) Zbl 1361.11072 Bouganis, Thanasis (ed.) et al., Iwasawa theory 2012. State of the art and recent advances. Selected papers based on the presentations at the conference, Heidelberg, Germany, July 30 – August 3, 2012. Berlin: Springer (ISBN 978-3-642-55244-1/hbk; 978-3-642-55245-8/ebook). Contributions in Mathematical and Computational Sciences 7, 221-226 (2014). MSC: 11R29 11R23 PDF BibTeX XML Cite \textit{T. Fukuda} et al., Contrib. Math. Comput. Sci. 7, 221--226 (2014; Zbl 1361.11072) Full Text: DOI
Lamplugh, Jack Triviality of the \(\ell\)-class groups in \(\mathbb{Z}_{p}\)-extensions of \(\mathbb{Q}(\sqrt{-1})\) for split primes \(p \equiv 1\) modulo 4. (English) Zbl 1296.11142 Math. Proc. Camb. Philos. Soc. 157, No. 1, 169-188 (2014). MSC: 11R29 11R06 11R27 PDF BibTeX XML Cite \textit{J. Lamplugh}, Math. Proc. Camb. Philos. Soc. 157, No. 1, 169--188 (2014; Zbl 1296.11142) Full Text: DOI
Ichimura, Humio; Nakajima, Shoichi; Sumida-Takahashi, Hiroki On the 2-adic Iwasawa lambda invariants of the \(p\)-cyclotomic fields and their quadratic twists. (English) Zbl 1318.11140 Int. J. Number Theory 10, No. 2, 283-296 (2014). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11R23 11R18 PDF BibTeX XML Cite \textit{H. Ichimura} et al., Int. J. Number Theory 10, No. 2, 283--296 (2014; Zbl 1318.11140) Full Text: DOI
Kitajima, Takahiro On the orders of even \(K\)-groups of rings of integers in cyclotomic \(\mathbb{Z}_{p}\)-extensions of \(\mathbb{Q}\). (English) Zbl 1331.11093 Int. J. Number Theory 9, No. 7, 1713-1724 (2013). MSC: 11R04 11R18 11R23 19D50 19F27 PDF BibTeX XML Cite \textit{T. Kitajima}, Int. J. Number Theory 9, No. 7, 1713--1724 (2013; Zbl 1331.11093) Full Text: DOI
Morisawa, Takayuki; Okazaki, Ryotaro Mahler measure and Weber’s class number problem in the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q\) for odd prime number \(p\). (English) Zbl 1280.11069 Tohoku Math. J. (2) 65, No. 2, 253-272 (2013). Reviewer: Roland Quême (Brax) (MR3079288) MSC: 11R29 11R06 11R18 11H06 PDF BibTeX XML Cite \textit{T. Morisawa} and \textit{R. Okazaki}, Tohoku Math. J. (2) 65, No. 2, 253--272 (2013; Zbl 1280.11069) Full Text: DOI Euclid
Ichimura, Humio Class number parity of a quadratic twist of a cyclotomic field of prime power conductor. (English) Zbl 1325.11110 Osaka J. Math. 50, No. 2, 563-572 (2013). MSC: 11R18 11R29 PDF BibTeX XML Cite \textit{H. Ichimura}, Osaka J. Math. 50, No. 2, 563--572 (2013; Zbl 1325.11110) Full Text: Euclid
Ichimura, Humio; Nakajima, Shoichi A note on the relative class number of the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q(\sqrt{-p})\). (English) Zbl 1333.11103 Proc. Japan Acad., Ser. A 88, No. 1, 16-20 (2012). MSC: 11R29 11R11 11R18 PDF BibTeX XML Cite \textit{H. Ichimura} and \textit{S. Nakajima}, Proc. Japan Acad., Ser. A 88, No. 1, 16--20 (2012; Zbl 1333.11103) Full Text: DOI Euclid
Ichimura, Humio; Nakajima, Shoichi On the 2-part of the class numbers of cyclotomic fields of prime power conductors. (English) Zbl 1247.11136 J. Math. Soc. Japan 64, No. 1, 317-342 (2012). Reviewer: Andreas Nickel (Bielefeld) MSC: 11R18 11R29 11R23 PDF BibTeX XML Cite \textit{H. Ichimura} and \textit{S. Nakajima}, J. Math. Soc. Japan 64, No. 1, 317--342 (2012; Zbl 1247.11136) Full Text: DOI
Fukuda, Takashi; Komatsu, Keiichi Weber’s class number problem in the cyclotomic \(\mathbb Z_2\)-extension of \(\mathbb Q\). II. (English) Zbl 1223.11133 J. Théor. Nombres Bordx. 22, No. 2, 359-368 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11R29 11R18 PDF BibTeX XML Cite \textit{T. Fukuda} and \textit{K. Komatsu}, J. Théor. Nombres Bordx. 22, No. 2, 359--368 (2010; Zbl 1223.11133) Full Text: DOI Link EuDML
Ichimura, Humio; Nakajima, Shoichi On the 2-part of the ideal class group of the cyclotomic \(\mathbb Z_p\)-extension over the rationals. (English) Zbl 1222.11126 Abh. Math. Semin. Univ. Hamb. 80, No. 2, 175-182 (2010). Reviewer: Andreas Nickel (Regensburg) MSC: 11R18 11R29 11R23 PDF BibTeX XML Cite \textit{H. Ichimura} and \textit{S. Nakajima}, Abh. Math. Semin. Univ. Hamb. 80, No. 2, 175--182 (2010; Zbl 1222.11126) Full Text: DOI
Sun, Hae-Sang Cuspidal class number of the tower of modular curves \(X_1(Np^n)\). (English) Zbl 1304.11051 Math. Ann. 348, No. 4, 909-927 (2010). MSC: 11G16 11B68 11G18 PDF BibTeX XML Cite \textit{H.-S. Sun}, Math. Ann. 348, No. 4, 909--927 (2010; Zbl 1304.11051) Full Text: DOI
Ichimura, Humio Hilbert-Speiser number fields and Stickelberger ideals. (English) Zbl 1205.11119 J. Théor. Nombres Bordx. 21, No. 3, 589-607 (2009). Reviewer: Henri Johnston (Cambridge) MSC: 11R33 11R18 PDF BibTeX XML Cite \textit{H. Ichimura}, J. Théor. Nombres Bordx. 21, No. 3, 589--607 (2009; Zbl 1205.11119) Full Text: DOI Numdam EuDML
Seo, Soogil Truncated Euler systems over imaginary quadratic fields. (English) Zbl 1226.11115 Nagoya Math. J. 195, 97-111 (2009). Reviewer: Lawrence C. Washington (College Park) MSC: 11R23 11R27 11R29 11G16 PDF BibTeX XML Cite \textit{S. Seo}, Nagoya Math. J. 195, 97--111 (2009; Zbl 1226.11115) Full Text: DOI Euclid
Sun, Hae-Sang Homological interpretation of a theorem of L. Washington. (English) Zbl 1210.11064 J. Number Theory 127, No. 1, 47-63 (2007). MSC: 11F67 11M06 PDF BibTeX XML Cite \textit{H.-S. Sun}, J. Number Theory 127, No. 1, 47--63 (2007; Zbl 1210.11064) Full Text: DOI
Horie, Kuniaki The ideal class group of the basic \(\mathbb Z_p\)-extension over an imaginary quadratic field. (English) Zbl 1128.11051 Tohoku Math. J. (2) 57, No. 3, 375-394 (2005). Reviewer: Lawrence C. Washington (College Park) MSC: 11R23 11R29 PDF BibTeX XML Cite \textit{K. Horie}, Tohoku Math. J. (2) 57, No. 3, 375--394 (2005; Zbl 1128.11051) Full Text: DOI
Skinner, Chris Modularity of Galois representations. (English) Zbl 1057.11032 J. Théor. Nombres Bordx. 15, No. 1, 367-381 (2003). Reviewer: Pham Huu Tiep (Gainesville) MSC: 11F80 11F41 PDF BibTeX XML Cite \textit{C. Skinner}, J. Théor. Nombres Bordx. 15, No. 1, 367--381 (2003; Zbl 1057.11032) Full Text: DOI Numdam EuDML
Vatsal, V. Special values of anticyclotomic \(L\)-functions. (English) Zbl 1065.11048 Duke Math. J. 116, No. 2, 219-261 (2003). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11G40 11F67 11F33 11G18 11R23 PDF BibTeX XML Cite \textit{V. Vatsal}, Duke Math. J. 116, No. 2, 219--261 (2003; Zbl 1065.11048) Full Text: DOI
Komatsu, Toru; Nakano, Shin On the Galois module structure of ideal class groups. (English) Zbl 1045.11079 Nagoya Math. J. 164, 133-146 (2001). Reviewer: Hideo Yokoi (Aichi) MSC: 11R29 11R21 PDF BibTeX XML Cite \textit{T. Komatsu} and \textit{S. Nakano}, Nagoya Math. J. 164, 133--146 (2001; Zbl 1045.11079) Full Text: DOI
Seo, Soogil Circular distributions and Euler systems. (English) Zbl 0995.11060 J. Number Theory 88, No. 2, 366-379 (2001). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R18 11R23 PDF BibTeX XML Cite \textit{S. Seo}, J. Number Theory 88, No. 2, 366--379 (2001; Zbl 0995.11060) Full Text: DOI
Skinner, C. M.; Wiles, A. J. Residually reducible representations and modular forms. (English) Zbl 1005.11030 Publ. Math., Inst. Hautes Étud. Sci. 89, 5-126 (1999). Reviewer: O.Ninnemann (Berlin) MSC: 11F80 11F11 PDF BibTeX XML Cite \textit{C. M. Skinner} and \textit{A. J. Wiles}, Publ. Math., Inst. Hautes Étud. Sci. 89, 5--126 (1999; Zbl 1005.11030) Full Text: DOI Numdam EuDML
Vatsal, V. Canonical periods and congruence formulae. (English) Zbl 0979.11027 Duke Math. J. 98, No. 2, 397-419 (1999). Reviewer: Kevin L.James (Clemson) MSC: 11F33 11F67 11F30 11G40 PDF BibTeX XML Cite \textit{V. Vatsal}, Duke Math. J. 98, No. 2, 397--419 (1999; Zbl 0979.11027) Full Text: DOI
Gillard, Roland Growth of class numbers in \({\mathbb{Z}}_{\ell}\)-extensions connected with imaginary quadratic fields. (Croissance du nombre de classes dans des \({\mathbb{Z}}_{\ell}\)-extensions liées aux corps quadratiques imaginaires.) (French) Zbl 0646.12003 Math. Ann. 279, No. 3, 349-372 (1988). Reviewer: Jean-François Jaulent (Talence) MSC: 11R18 11R23 11R27 11R11 PDF BibTeX XML Cite \textit{R. Gillard}, Math. Ann. 279, No. 3, 349--372 (1988; Zbl 0646.12003) Full Text: DOI EuDML
Sinnott, W. \(\Gamma\)-transforms of rational function measures on \(\mathbb Z_ S\). (English) Zbl 0637.12004 Invent. Math. 89, 139-157 (1987). Reviewer: Lawrence C. Washington (College Park) MSC: 11R23 11R18 11S80 PDF BibTeX XML Cite \textit{W. Sinnott}, Invent. Math. 89, 139--157 (1987; Zbl 0637.12004) Full Text: DOI EuDML
Kuz’min, L. V. Algebraic number fields. (English) Zbl 0621.12002 J. Sov. Math. 38, 1930-1988 (1987). MSC: 11-02 11Rxx 11Sxx 12Gxx PDF BibTeX XML Cite \textit{L. V. Kuz'min}, J. Sov. Math. 38, 1930--1988 (1987; Zbl 0621.12002) Full Text: DOI
Adachi, Norio Dedekind domains which are not obtainable as finite integral extensions of PID. (English) Zbl 0579.13009 Proc. Japan Acad., Ser. A 61, 281-282 (1985). Reviewer: C.U.Jensen MSC: 13F05 13F10 PDF BibTeX XML Cite \textit{N. Adachi}, Proc. Japan Acad., Ser. A 61, 281--282 (1985; Zbl 0579.13009) Full Text: DOI
Sinnott, W. On the \(\mu\)-invariant of the \(\Gamma\)-transform of a rational function. (English) Zbl 0531.12004 Invent. Math. 75, 273-282 (1984). Reviewer: Lawrence C. Washington (College Park) MSC: 11R23 11S40 11S80 11R58 11B39 PDF BibTeX XML Cite \textit{W. Sinnott}, Invent. Math. 75, 273--282 (1984; Zbl 0531.12004) Full Text: DOI EuDML
Kamienny, S.; Stevens, G. Special values of L-functions attached to \(X_ 1(N)\). (English) Zbl 0519.14018 Compos. Math. 49, 121-142 (1983). MSC: 14G10 14H25 PDF BibTeX XML Cite \textit{S. Kamienny} and \textit{G. Stevens}, Compos. Math. 49, 121--142 (1983; Zbl 0519.14018) Full Text: Numdam EuDML
Rubin, Karl Congruences for special values of L-functions of elliptic curves with complex multiplication. (English) Zbl 0513.14012 Invent. Math. 71, 339-364 (1983). MSC: 14G10 14H52 14K22 14G25 14H25 14H45 PDF BibTeX XML Cite \textit{K. Rubin}, Invent. Math. 71, 339--364 (1983; Zbl 0513.14012) Full Text: DOI EuDML
Friedman, Eduardo C. Ideal class groups in basic \(\mathbb Z_{p_1}\times\dots\times\mathbb Z_{p_s}\)-extensions of abelian number fields. (English) Zbl 0495.12007 Invent. Math. 65, 425-440 (1982). Reviewer: S. Kanemitsu MSC: 11R23 11R18 11R29 PDF BibTeX XML Cite \textit{E. C. Friedman}, Invent. Math. 65, 425--440 (1982; Zbl 0495.12007) Full Text: DOI EuDML
Lang, Serge Units and class groups in number theory and algebraic geometry. (English) Zbl 0482.12002 Bull. Am. Math. Soc., New Ser. 6, 253-316 (1982). Reviewer: Serge Lang MSC: 11R27 11R29 11-02 11R42 14H25 11R18 11G18 PDF BibTeX XML Cite \textit{S. Lang}, Bull. Am. Math. Soc., New Ser. 6, 253--316 (1982; Zbl 0482.12002) Full Text: DOI
Mazur, B. On the arithmetic of special values of L functions. (English) Zbl 0426.14009 Invent. Math. 55, 207-240 (1979). MSC: 14G10 14G05 14G25 11R06 11B39 PDF BibTeX XML Cite \textit{B. Mazur}, Invent. Math. 55, 207--240 (1979; Zbl 0426.14009) Full Text: DOI EuDML