Harron, Robert; Holmes, Erik; Vemulapalli, Sameera Shapes of unit lattices in \(D_p\)-number fields. arXiv:2501.12504 Preprint, arXiv:2501.12504 [math.NT] (2025). MSC: 11R27 11R18 11R33 × Cite Format Result Cite Full Text: arXiv
Hamahata, Yoshinori Normal bases for function fields. (English) Zbl 07970430 Bull. Aust. Math. Soc. 110, No. 1, 44-55 (2024). MSC: 11F52 11G16 11R60 12F05 × Cite Format Result Cite Review PDF Full Text: DOI
Morisawa, Takayuki Filtrations of relative units in the cyclotomic \(\mathbb{Z}_p\)-extension of \(\mathbb{Q}\). (English) Zbl 07960199 J. Ramanujan Math. Soc. 39, No. 3, 239-251 (2024). MSC: 11R27 11R18 × Cite Format Result Cite Review PDF Full Text: Link
Tsuji, Takae Semi-local units modulo cyclotomic units in the cyclotomic \(\mathbb{Z}_2\)-extensions. (English. French summary) Zbl 07948973 J. Théor. Nombres Bordx. 36, No. 2, 445-479 (2024). MSC: 11R23 × Cite Format Result Cite Review PDF Full Text: DOI
Burns, David; Macias Castillo, Daniel; Seo, Soogil On Weil-Stark elements. I: Construction and general properties. (English) Zbl 07947525 J. Lond. Math. Soc., II. Ser. 110, No. 5, Article ID e70001, 39 p. (2024). Reviewer: James E. Carter (Charleston) MSC: 11R27 11R29 11R34 11R33 × Cite Format Result Cite Review PDF Full Text: DOI
Chatterjee, Tapas; Garg, Sonam Transcendental nature of \(p\)-adic digamma values. (English) Zbl 07937599 Res. Number Theory 10, No. 4, Paper No. 79, 19 p. (2024). Reviewer: József Sándor (Cluj-Napoca) MSC: 11E95 11J81 11J86 11J91 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Biasse, Jean-François; Fieker, Claus; Hofmann, Tommy; Youmans, William An algorithm for solving the principal ideal problem with subfields. (English) Zbl 07913850 Adv. Math. Commun. 18, No. 6, 1785-1809 (2024). MSC: 11Y16 20C05 11R32 11R29 11R04 11Y40 11R18 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Sumida-Takahashi, Hiroki; Furuya, Naoki; Kitano, Kodai Greenberg’s generalized conjecture and pairings of \(p\)-units in the \(4p\)-cyclotomic field. (English) Zbl 1543.11100 J. Ramanujan Math. Soc. 39, No. 1, 79-90 (2024). MSC: 11R23 11R18 11R29 11R70 × Cite Format Result Cite Review PDF Full Text: Link
Mouhib, A.; Rouas, S. Correction to: On the rank of the 2-class group of some imaginary biquadratic number fields. (English) Zbl 07829370 Acta Math. Hung. 172, No. 1, 287 (2024). MSC: 11R11 11R16 11R18 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
de Araujo, Robson Ricardo An upper bound on the covering radius of the logarithmic lattice for cyclotomic number fields. (English) Zbl 1545.11064 Discrete Math. 347, No. 1, Article ID 113665, 6 p. (2024). Reviewer: Gabriele Nebe (Aachen) MSC: 11H31 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Gras, Georges Notion of abelian arithmetic \(\varphi\)-objects for the study of \(p\)-class groups and \(p\)-ramified torsion groups. (English) Zbl 1528.11113 North-West. Eur. J. Math. 9, 109-199 (2023). MSC: 11R18 11R29 11R27 11R37 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Sumida-Takahashi, Hiroki A generalized problem associated to the Kummer-Vandiver conjecture. (English) Zbl 1530.11086 Arnold Math. J. 9, No. 3, 381-391 (2023). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R23 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Chems-Eddin, Mohamed Mahmoud; El Fadil, Lhoussain The 2-class group of certain families of imaginary triquadratic fields. (English) Zbl 1518.11075 Math. Slovaca 73, No. 4, 835-848 (2023). MSC: 11R18 11R29 11R11 11R16 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Garcia, Vitor Araujo; Ferraz, Raul Antonio Units in some group rings over the ring of \(p\)-cyclotomic integers. (English) Zbl 1522.20022 J. Algebra Appl. 22, No. 5, Article ID 2350104, 8 p. (2023). Reviewer: Christoph Winges (Regensburg) MSC: 20C05 16U60 16S34 × Cite Format Result Cite Review PDF Full Text: DOI
Biasse, Jean-François; Fieker, Claus; Hofmann, Tommy; Page, Aurel Norm relations and computational problems in number fields. (English) Zbl 1530.11098 J. Lond. Math. Soc., II. Ser. 105, No. 4, 2373-2414 (2022). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11Y16 11Y40 20C05 11R32 11R29 11R04 11R18 11R27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chems-Eddin, Mohamed Mahmoud; Zekhnini, Abdelkader; Azizi, Abdelmalek Unit groups of some multiquadratic number fields of degree 16. (English) Zbl 1514.11070 São Paulo J. Math. Sci. 16, No. 2, 1091-1096 (2022). Reviewer: Artūras Dubickas (Vilnius) MSC: 11R04 11R27 11R29 11R37 × Cite Format Result Cite Review PDF Full Text: DOI
Fedorov, G. V. On the problem of describing elements of elliptic fields with a periodic expansion into a continued fraction over quadratic fields. (English. Russian original) Zbl 1503.11102 Dokl. Math. 106, No. 1, 259-264 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 505, 56-62 (2022). MSC: 11J70 11R58 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Sharifi, Romyar T. Reciprocity maps with restricted ramification. (English) Zbl 1523.11205 Trans. Am. Math. Soc. 375, No. 8, 5361-5392 (2022). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R34 11R23 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mouhib, A.; Rouas, S. On the rank of the 2-class group of some imaginary biquadratic number fields. (English) Zbl 1513.11179 Acta Math. Hung. 167, No. 1, 295-308 (2022). Reviewer: Nikolai L. Manev (Sofia) MSC: 11R11 11R16 11R18 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
Chatterjee, Tapas; Dhillon, Sonika On a conjecture of Murty-Saradha about digamma values. (English) Zbl 1502.11080 Monatsh. Math. 199, No. 1, 23-43 (2022). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11J81 11J72 11J86 11J91 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Seo, Soogil On universal norm elements and a problem of Coleman. (English) Zbl 1501.11100 Mosc. Math. J. 22, No. 1, 121-132 (2022). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R23 11R37 11R18 11R34 11R27 11S25 × Cite Format Result Cite Review PDF Full Text: Link
Chems-Eddin, Mohamed Mahmoud Unit groups of some multiquadratic number fields and 2-class groups. (English) Zbl 1513.11178 Period. Math. Hung. 84, No. 2, 235-249 (2022). Reviewer: Nikolai L. Manev (Sofia) MSC: 11R04 11R27 11R29 11R37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wu, Hai-Liang; She, Yue-Feng On a polynomial involving roots of unity and its applications. (English) Zbl 1500.11077 Int. J. Number Theory 18, No. 8, 1749-1763 (2022). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R18 11R11 11R27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chems-Eddin, Mohamed Mahmoud The rank of the 2-class group of some fields with large degree. (English) Zbl 1500.11081 Algebra Colloq. 29, No. 2, 181-188 (2022). Reviewer: Claude Levesque (Québec) MSC: 11R29 11R23 11R27 11R04 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pagani, Lorenzo Greenberg’s conjecture for real quadratic fields and the cyclotomic \(\mathbb{Z}_2\)-extensions. (English) Zbl 1522.11114 Math. Comput. 91, No. 335, 1437-1467 (2022). MSC: 11R23 11R29 11Y40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Smirnov, A. L. On explicit units in Kummer’s tower. (English. Russian original) Zbl 1507.11099 J. Math. Sci., New York 261, No. 4, 574-583 (2022); translation from Zap. Nauchn. Semin. POMI 490, 109-123 (2020). Reviewer: Isabelle Dubois (Metz) MSC: 11R20 11R18 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Azizi, Abdelmalek; Elmouhib, Fouad; Talbi, Mohamed 5-rank of ambiguous class groups of quintic Kummer extensions. (English) Zbl 1522.11117 Proc. Indian Acad. Sci., Math. Sci. 132, No. 1, Paper No. 12, 14 p. (2022). MSC: 11R29 11R16 11R18 11R27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hofer, Martin; Kleine, Sören On two conjectures of Gross for large vanishing orders. (English) Zbl 1505.11142 Monatsh. Math. 197, No. 1, 85-109 (2022). Reviewer: Robert W. van der Waall (Huizen) MSC: 11R23 11-02 11R20 11R18 11R27 11R37 11S40 11R80 11F41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Greither, Cornelius; Kučera, Radan On the compositum of orthogonal cyclic fields of the same odd prime degree. (English) Zbl 1487.11099 Can. J. Math. 73, No. 6, 1506-1530 (2021). Reviewer: Claude Levesque (Québec) MSC: 11R20 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Dummit, David S.; Kisilevsky, Hershy The unit signature rank deficiency is unbounded over cyclotomic fields. (English) Zbl 1483.11245 Pac. J. Math. 314, No. 2, 259-267 (2021). Reviewer: Günter Lettl (Graz) MSC: 11R27 11R80 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Azizi, Abdelmalek; Chems-Eddin, Mohamed Mahmoud; Zekhnini, Abdelkader On the rank of the 2-class group of some imaginary triquadratic number fields. (English) Zbl 1480.11137 Rend. Circ. Mat. Palermo (2) 70, No. 3, 1751-1769 (2021). Reviewer: Claude Levesque (Québec) MSC: 11R11 11R16 11R18 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Arul, Vishal On the \(\ell\)-adic valuation of certain Jacobi sums. (English) Zbl 1489.11113 J. Théor. Nombres Bordx. 33, No. 2, 607-625 (2021). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11L05 11R18 11R27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Greither, Cornelius; Kučera, Radan Washington units, semispecial units, and annihilation of class groups. (English) Zbl 1479.11186 Manuscr. Math. 166, No. 1-2, 277-286 (2021). Reviewer: Günter Lettl (Graz) MSC: 11R20 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Chems-Eddin, Mohamed Mahmoud; Azizi, Abdelmalek; Zekhnini, Abdelkader Unit groups and Iwasawa lambda invariants of some multiquadratic number fields. (English) Zbl 1468.11223 Bol. Soc. Mat. Mex., III. Ser. 27, No. 1, Paper No. 24, 16 p. (2021). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R20 11R04 11R23 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
Burns, David; Seo, Soogil On circular distributions and a conjecture of Coleman. (English) Zbl 1473.11199 Isr. J. Math. 241, No. 1, 343-393 (2021). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11R18 11R27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kirshanova, E. A.; Malygina, E. S.; Novoselov, S. A.; Olefirenko, D. O. An algorithm for computing the Stickelberger ideal for multiquadratic number fields. (Russian. English summary) Zbl 1459.11215 Prikl. Diskretn. Mat. 2021, No. 51, 9-30 (2021). MSC: 11R27 11R18 11R20 × Cite Format Result Cite Review PDF Full Text: DOI MNR
Kashio, Tomokazu; Yoshizaki, Hyuga Minimal relative units of the cyclotomic \(\mathbb Z_2\)-extension. arXiv:2107.08587 Preprint, arXiv:2107.08587 [math.NT] (2021). MSC: 11R27 11R29 11R18 11Y40 × Cite Format Result Cite Full Text: arXiv
Lee, Wan; Seo, Soogil On the arithmetic of modified idèle class groups. (English. Russian original) Zbl 1456.11211 Izv. Math. 84, No. 3, 545-591 (2020); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 3, 119-167 (2020). MSC: 11R23 11R27 11R29 11R37 11S25 11S31 × Cite Format Result Cite Review PDF Full Text: DOI
Mihăilescu, Preda The charm of units. I: On the Kummer-Vandiver conjecture. Extended abstract. (English) Zbl 1458.11155 Chakraborty, Kalyan (ed.) et al., Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4–7, 2017. Singapore: Springer. 73-87 (2020). Reviewer: C. P. Anil Kumar (Chennai) MSC: 11R27 11R23 11R70 × Cite Format Result Cite Review PDF Full Text: DOI
Dummit, David S. A note on the equivalence of the parity of class numbers and the signature ranks of units in cyclotomic fields. (English) Zbl 1453.11138 Nagoya Math. J. 238, 206-214 (2020). MSC: 11R18 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Morisawa, Takayuki; Okazaki, Ryotaro Filtrations of units of Viète field. (English) Zbl 1453.11145 Int. J. Number Theory 16, No. 5, 1067-1079 (2020). Reviewer: C. P. Anil Kumar (Chennai) MSC: 11R27 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Chatterjee, Tapas; Dhillon, Sonika Linear independence of logarithms of cyclotomic numbers and a conjecture of Livingston. (English) Zbl 1446.11137 Can. Math. Bull. 63, No. 1, 31-45 (2020). Reviewer: Mahadi Ddamulira (Saarbrücken) MSC: 11J81 11J72 11J86 11J91 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Girstmair, Kurt Linear relations among asymptotic frequencies in continued fractions. (English) Zbl 1440.11146 Monatsh. Math. 191, No. 1, 77-91 (2020). Reviewer: Symon Serbenyuk (Kyiv) MSC: 11K50 11J81 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
El Kati, Mohamed; Oukhaba, Hassan Polynomials defining many units in function fields. (English) Zbl 1452.11138 Acta Arith. 190, No. 4, 351-361 (2019). MSC: 11R60 11R27 11R58 16U60 × Cite Format Result Cite Review PDF Full Text: DOI
Nguyen, Dong Quan Ngoc Representation of units in cyclotomic function fields. (English) Zbl 1439.11287 Int. J. Number Theory 15, No. 7, 1385-1401 (2019). Reviewer: Gabriel D. Villa Salvador (Ciudad de México) MSC: 11R60 11R27 11R58 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dummit, David S.; Dummit, Evan P.; Kisilevsky, Hershy Signature ranks of units in cyclotomic extensions of abelian number fields. (English) Zbl 1453.11139 Pac. J. Math. 298, No. 2, 285-298 (2019). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11R18 11R27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Aleev, Rifkhat Zhalyalovich; Mitina, Ol’ga Viktorovna; Khanenko, Tat’yana Aleksandrovna Local units of integer group ring of cyclic group of order 64 for character with character field \(\mathbb{Q}_{64}\). (Russian. English summary) Zbl 1465.16036 Chelyabinskiĭ Fiz.-Mat. Zh. 3, No. 3, 253-275 (2018). MSC: 16U60 16S34 20C05 × Cite Format Result Cite Review PDF Full Text: DOI MNR
Kashio, Tomokazu Fermat curves and a refinement of the reciprocity law on cyclotomic units. (English) Zbl 1436.11060 J. Reine Angew. Math. 741, 255-273 (2018). MSC: 11G05 11A15 11R18 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kuz’min, L. V. Local and global universal norms in the cyclotomic \( {\mathbb Z}_\ell\)-extension of an algebraic number field. (English. Russian original) Zbl 1439.11277 Izv. Math. 82, No. 3, 532-548 (2018); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 82, No. 3, 90-107 (2018). MSC: 11R18 11R23 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Gras, Georges The \(p\)-adic Kummer-Leopoldt constant: normalized \(p\)-adic regulator. (English) Zbl 1393.11071 Int. J. Number Theory 14, No. 2, 329-337 (2018). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R27 11R37 11R29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kashio, Tomokazu Stark’s conjecture over the rational number field and CM-periods of Fermat curves. (English) Zbl 1415.11157 RIMS Kôkyûroku Bessatsu B64, 93-106 (2017). MSC: 11R27 11M06 11R42 11S80 14H45 × Cite Format Result Cite Review PDF
Tsuji, Takae On the Iwasawa \(\lambda\)-invariants of cyclotomic \({\mathbb Z}_2\)-extensions of real abelian fields. (English) Zbl 1415.11156 RIMS Kôkyûroku Bessatsu B64, 67-76 (2017). MSC: 11R23 × Cite Format Result Cite Review PDF
Jaulent, Jean-François On the cyclotomic norms and the Leopoldt and Gross-Kuz’min conjectures. (Sur les normes cyclotomiques et les conjectures de Leopoldt et de Gross-Kuz’min.) (French. English summary) Zbl 1432.11161 Ann. Math. Qué. 41, No. 1, 119-140 (2017). MSC: 11R23 11R18 11R37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Jaulent, Jean-François Naive cyclotomic norms and logarithmic units. (Normes cyclotomiques naïves et unités logarithmiques.) (French. English summary) Zbl 1430.11147 Arch. Math. 108, No. 6, 545-554 (2017). MSC: 11R23 11R27 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Nguyen Quang Do, Thong On a weak form of Greenberg’s conjecture. II. (Sur une forme faible de la conjecture de Greenberg. II.) (French. English summary) Zbl 1377.11112 Int. J. Number Theory 13, No. 4, 1061-1070 (2017). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11R23 × Cite Format Result Cite Review PDF Full Text: DOI
Anglès, Bruno; Tavares Ribeiro, Floric Arithmetic of function field units. (English) Zbl 1382.11043 Math. Ann. 367, No. 1-2, 501-579 (2017). Reviewer: Liang-Chung Hsia (Taipei) MSC: 11G09 11R58 11R60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kučera, Radan On a theorem of Thaine. (English) Zbl 1421.11088 J. Number Theory 173, 416-424 (2017). MSC: 11R20 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
Aleev, Rifkhat Zhalyalovich; Mitina, Ol’ga Viktorovna; Khristenko, Ekaterina Andreevna Congruence modulo 2 of circular units in the fields \(Q_{16}\) and \(Q_{32}\). (Russian. English summary) Zbl 1464.11117 Chelyabinskiĭ Fiz.-Mat. Zh. 1, No. 4, 8-29 (2016). MSC: 11R27 11R18 16S34 16U60 × Cite Format Result Cite Review PDF Full Text: MNR
Kučera, Radan The circular units and the Stickelberger ideal of a cyclotomic field revisited. (English) Zbl 1358.11124 Acta Arith. 174, No. 3, 217-238 (2016). Reviewer: Henri Johnston (Exeter) MSC: 11R27 11R18 × Cite Format Result Cite Review PDF Full Text: DOI Link
Broche, Osnel; del Río, Ángel Polynomials defining many units. (English) Zbl 1356.16030 Math. Z. 283, No. 3-4, 1195-1200 (2016). Reviewer: János Kurdics (Nyíregyháza) MSC: 16U60 20C05 16S34 12E10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhang, Xianke Algebraic number theory. 2nd edition. (English) Zbl 1353.11002 Beijing: Higher Education Press; Oxford: Alpha Science International (ISBN 978-1-78332-208-4/hbk). not consecutively paged. (2016). Reviewer: Nikolai L. Manev (Sofia) MSC: 11-01 11Rxx 11Sxx × Cite Format Result Cite Review PDF
Kučera, Radan; Salami, Azar Circular units of an abelian field ramified at three primes. (English) Zbl 1408.11106 J. Number Theory 163, 296-315 (2016). MSC: 11R20 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Ichimura, Humio On a duality of Gras between totally positive and primary cyclotomic units. (English) Zbl 1408.11109 Math. J. Okayama Univ. 58, 125-132 (2016). MSC: 11R33 11R18 11R29 × Cite Format Result Cite Review PDF Full Text: Link
Jespers, Eric; del Río, Ángel Group ring groups. Volume 2: Structure theorems of unit groups. (English) Zbl 1338.16002 De Gruyter Textbook. Berlin: De Gruyter (ISBN 978-3-11-041149-2/pbk; 978-3-11-041150-8/ebook). x, 217 p. (2016). Reviewer: János Kurdics (Nyíregyháza) MSC: 16-02 20-02 16U60 16S34 20C05 16H10 × Cite Format Result Cite Review PDF Full Text: DOI
Jespers, Eric; del Río, Ángel Group ring groups. Volume 1: Orders and generic constructions of units. (English) Zbl 1338.16001 De Gruyter Textbook. Berlin: De Gruyter (ISBN 978-3-11-037278-6/pbk; 978-3-11-037294-6/ebook). xii, 447 p. (2016). Reviewer: János Kurdics (Nyíregyháza) MSC: 16-02 20-02 16U60 16S34 20C05 16H10 × Cite Format Result Cite Review PDF Full Text: DOI
Greither, Cornelius; Kučera, Radan Annihilators for the class group of a cyclic field of prime power degree. III. (English) Zbl 1374.11087 Publ. Math. Debr. 86, No. 3-4, 401-421 (2015). Reviewer: Günter Lettl (Graz) MSC: 11R20 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
Seo, Soogil On the conjectures of Gross and Leopoldt. (English) Zbl 1411.11100 Math. Res. Lett. 22, No. 5, 1509-1540 (2015). MSC: 11R18 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Ichimura, Humio Semi-local units at \(p\) of a cyclotomic \(\mathbb{Z}_p\)-extension congruent to 1 modulo \(\zeta_p - 1\). (English) Zbl 1336.11073 Hokkaido Math. J. 44, No. 3, 397-407 (2015). Reviewer: Alexandru Ciolan (Bonn) MSC: 11S23 11R18 11R23 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Ferraz, Raul Antonio; Kitani, Patrícia Massae Units of \(\mathbb ZC_{p^n}\). (English) Zbl 1336.16039 Commun. Algebra 43, No. 11, 4936-4950 (2015). Reviewer: János Kurdics (Nyíregyháza) MSC: 16U60 16S34 20C05 11R27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gomez, Clément Refined class number formulas for elliptic units. (English. French summary) Zbl 1400.11144 Ann. Math. Qué. 39, No. 1, 1-24 (2015). MSC: 11R29 11G16 11R04 11R11 11R18 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Rivertz, H. J. Self-similar aperiodic patterns with 9-fold symmetry. (English) Zbl 1325.52014 J. Number Theory 155, 100-110 (2015). Reviewer: Wolfgang Globke (Adelaide) MSC: 52C20 52C23 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Anglès, Bruno; Taelman, Lenny; Bosser, Vincent Arithmetic of characteristic \(p\) special \(L\)-values. (English) Zbl 1328.11065 Proc. Lond. Math. Soc. (3) 110, No. 4, 1000-1032 (2015). Reviewer: Gabriel D. Villa-Salvador (México D. F.) MSC: 11G09 11M38 11R60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kuz’min, L. V. On a new type of \(\ell\)-adic regulator for algebraic number fields (the \(\ell\)-adic regulator without logarithms). (English. Russian original) Zbl 1325.11115 Izv. Math. 79, No. 1, 109-144 (2015); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 79, No. 1, 115-152 (2015). Reviewer: Wei Feng (Beijing) MSC: 11R23 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Yuanlin; Parmenter, M. M.; Yuan, Pingzhi On \(*\)-clean group rings. (English) Zbl 1318.16024 J. Algebra Appl. 14, No. 1, Article ID 1550004, 11 p. (2015). Reviewer: Todor Mollov (Plovdiv) MSC: 16S34 20C05 16W10 16U60 × Cite Format Result Cite Review PDF Full Text: DOI
Kim, Jae Moon; Ryu, Jado A note on Ennola relation. (English) Zbl 1357.11110 Taiwanese J. Math. 18, No. 5, 1653-1661 (2014). MSC: 11R27 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Seo, Soogil On finite layers of \(\mathbb{Z}_l\)-extensions and \(K_2\). (English) Zbl 1371.11144 J. Number Theory 145, 153-180 (2014). MSC: 11R27 11R23 11R70 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Küçüksakallı, Ömer On the units generated by Weierstrass forms. (English) Zbl 1296.11069 LMS J. Comput. Math. 17A, Spec. Iss., 303-313 (2014). MSC: 11G16 11R29 11Y40 × Cite Format Result Cite Review PDF Full Text: DOI
Greither, Cornelius; Kučera, Radan Linear forms on Sinnott’s module. (English) Zbl 1309.11079 J. Number Theory 141, 324-342 (2014). Reviewer: Günter Lettl (Graz) MSC: 11R33 11R20 × Cite Format Result Cite Review PDF Full Text: DOI
Eschenburg, J.-H.; Rivertz, H. J. Self similarity of dihedral tilings. (English) Zbl 1296.52012 J. Algebra 405, 69-74 (2014). MSC: 52C20 52C23 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Kuz’min, L. V. On \( \ell\)-adic logarithms of Gauss sums. (English. Russian original) Zbl 1314.11075 Izv. Math. 78, No. 3, 531-553 (2014); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 78, No. 3, 111-134 (2014). Reviewer: Henri Johnston (Exeter) MSC: 11T24 11R18 11R23 × Cite Format Result Cite Review PDF Full Text: DOI
Malik, Amita; Stan, Florin; Zaharescu, Alexandru The Siegel norm, the length function and character values of finite groups. (English) Zbl 1301.20007 Indag. Math., New Ser. 25, No. 3, 475-486 (2014). Reviewer: Robert W. van der Waall (Huizen) MSC: 20C15 11R27 11R04 11L40 × Cite Format Result Cite Review PDF Full Text: DOI
All, Timothy On the \(p\)-adic completion of the units of a real abelian number field. (English) Zbl 1292.11120 J. Number Theory 136, 1-21 (2014). Reviewer: Günter Lettl (Graz) MSC: 11R18 11R33 11S23 × Cite Format Result Cite Review PDF Full Text: DOI
Solomon, David Some new maps and ideals in classical Iwasawa theory with applications. (English) Zbl 1292.11122 Acta Arith. 162, No. 2, 101-140 (2014). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R18 11R27 11R29 11R42 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Jespers, Eric; del Río, Ángel; Van Gelder, Inneke Writing units of integral group rings of finite abelian groups as a product of Bass units. (English) Zbl 1312.16034 Math. Comput. 83, No. 285, 461-473 (2014). Reviewer: Ernesto Spinelli (Roma) MSC: 16U60 20C05 16S34 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Herman, Jan Annihilators of the class group of a compositum of quadratic fields. (English) Zbl 1299.11079 Arch. Math., Brno 49, No. 4, 209-222 (2013). Reviewer: Radan Kučera (Brno) MSC: 11R20 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI EMIS
Kim, Jae Moon; Ryu, Jado On the Washington subgroup of the unit group of certain abelian fields. (English) Zbl 1290.11150 Ramanujan J. 32, No. 3, 315-328 (2013). Reviewer: Roland Quême (Brax) MSC: 11R27 11R18 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
Murty, M. Ram The work of K. Ramachandra in algebraic number theory. (English) Zbl 1303.11004 Hardy-Ramanujan J. 34-35(2011-2012), 11-19 (2013). Reviewer: Günter Lettl (Graz) MSC: 11-03 11R27 11R29 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Karimilla Bi, N. Representations and matrix units for the cyclotomic Brauer algebras of \(G(r,p,n)\) type. (English) Zbl 1347.20003 Aligarh Bull. Math. 31, No. 1-2, 67-108 (2012). MSC: 20C08 16G20 20F55 05E10 × Cite Format Result Cite Review PDF
Dalawat, Chandan Singh Primary units cyclotomic fields. (English) Zbl 1295.11123 Ann. Sci. Math. Qué. 36, No. 1, 93-98 (2012). MSC: 11R27 11R18 12J25 × Cite Format Result Cite Review PDF Full Text: arXiv
Gras, Georges; Quême, Roland Vandiver papers on cyclotomy revisited and Fermat’s last theorem. (English) Zbl 1309.11028 Algèbre et théorie des nombres 2012/2. Besançon: Presses Universitaires de Franche-Comté. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2012/2, 47-111 (2012). Reviewer: Lawrence C. Washington (College Park) MSC: 11D41 11R18 11R44 11R45 × Cite Format Result Cite Review PDF Full Text: Link
Stewart, C. L. Exceptional units and cyclic resultants. (English) Zbl 1270.11114 Acta Arith. 155, No. 4, 407-418 (2012). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R27 11B83 11J68 × Cite Format Result Cite Review PDF Full Text: DOI
Büyükboduk, Kâzim Height pairings, exceptional zeros and Rubin’s formula: the multiplicative group. (English) Zbl 1246.11171 Comment. Math. Helv. 87, No. 1, 71-111 (2012). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 11R23 11R34 11R42 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sharifi, Romyar A reciprocity map and the two-variable \(p\)-adic \(L\)-function. (English) Zbl 1248.11085 Ann. Math. (2) 173, No. 1, 251-300 (2011). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 11R23 11F67 11R34 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kim, Jae Moon; Ryu, Jado Construction of a certain circular unit and its applications. (English) Zbl 1229.11135 J. Number Theory 131, No. 4, 737-744 (2011). Reviewer: Bouchaïb Sodaïgui (Valenciennes) MSC: 11R18 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
Mazur, Barry; Rubin, Karl Refined class number formulas and Kolyvagin systems. (English) Zbl 1225.11144 Compos. Math. 147, No. 1, 56-74 (2011). Reviewer: Florin Nicolae (Berlin) MSC: 11R29 11R42 11R27 11R37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shi, Jun; Xia, Jianguo Power integral bases of cyclotomic field \(\mathbb Q(\zeta_{40})\). (Chinese. English summary) Zbl 1240.11130 J. Nanjing Norm. Univ., Nat. Sci. Ed. 33, No. 4, 28-32 (2010). MSC: 11R04 11R18 11R27 × Cite Format Result Cite Review PDF
Hambleton, S.; Scharaschkin, V. Quadratic reciprocity via resultants. (English) Zbl 1206.11004 Int. J. Number Theory 6, No. 6, 1413-1417 (2010). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11A15 11C08 × Cite Format Result Cite Review PDF Full Text: DOI
Morisawa, Takayuki Mahler measure of the Horie unit and Weber’s class number problem in the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q\). (English) Zbl 1201.11104 Komatsu, Takao (ed.), Diophantine analysis and related fields 2010. DARF–2010. Proceedings of the conference, Musashino, Tokyo, Japan, March 4–5, 2010. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0815-9). AIP Conference Proceedings 1264, 52-61 (2010). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R29 11Y40 11R06 × Cite Format Result Cite Review PDF Full Text: DOI
Nuccio, Filippo Alberto Edoardo Cyclotomic units and class groups in \(\mathbb Z_p\)-extensions of real abelian fields. (English) Zbl 1279.11108 Math. Proc. Camb. Philos. Soc. 148, No. 1, 93-106 (2010). Reviewer: Günter Lettl (Graz) MSC: 11R23 11R18 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL