Dasgupta, Samit; Kakde, Mahesh On the Brumer-Stark conjecture and refinements. (English) Zbl 1533.11189 Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 3. Sections 1–4. Berlin: European Mathematical Society (EMS). 1768-1799 (2023). MSC: 11R37 11R42 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rivero, Óscar Derivatives of Beilinson-Flach classes, Gross-Stark formulas and a \(p\)-adic Harris-Venkatesh conjecture. (English) Zbl 1540.11052 Doc. Math. 28, No. 1, 105-131 (2023). MSC: 11F67 11S40 19F27 × Cite Format Result Cite Review PDF Full Text: DOI
Kopp, Gene S. A Kronecker limit formula for indefinite zeta functions. (English) Zbl 1531.11084 Res. Math. Sci. 10, No. 2, Paper No. 24, 21 p. (2023). Reviewer: Roma Kačinskaitė (Vilnius) MSC: 11M41 11R42 11F27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dasgupta, Samit; Kakde, Mahesh On the Brumer-Stark conjecture. (English) Zbl 1525.11128 Ann. Math. (2) 197, No. 1, 289-388 (2023). Reviewer: Lawrence C. Washington (College Park) MSC: 11R23 11R29 11R42 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kopp, Gene S. SIC-POVMs and the Stark conjectures. (English) Zbl 1489.11191 Int. Math. Res. Not. 2021, No. 18, 13812-13838 (2021). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R37 11R42 32S22 81P15 81R05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kopp, Gene S. Indefinite zeta functions. (English) Zbl 1470.11058 Res. Math. Sci. 8, No. 1, Paper No. 17, 34 p. (2021). MSC: 11E45 11F27 11M41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dasgupta, Samit; Kakde, Mahesh On the rank one Gross-Stark conjecture for quadratic extensions and the Deligne-Ribet \(q\)-expansion principle. (English) Zbl 1475.11210 Kurihara, Masato (ed.) et al., Development of Iwasawa theory – the centennial of K. Iwasawa’s birth. Proceedings of the international conference “Iwasawa 2017”, University of Tokyo, Tokyo, Japan, July 19–28, 2017. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 86, 243-254 (2020). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R42 11F41 11F80 11R23 × Cite Format Result Cite Review PDF Full Text: DOI
Kashio, Tomokazu A period-ring-valued gamma function and a refinement of the reciprocity law on Stark units. (English) Zbl 1461.11150 RIMS Kôkyûroku Bessatsu B83, 169-181 (2020). MSC: 11R27 11R42 14F30 14K22 × Cite Format Result Cite Review PDF Full Text: Link
Appleby, Marcus; Flammia, Steven; McConnell, Gary; Yard, Jon Generating ray class fields of real quadratic fields via complex equiangular lines. (English) Zbl 1442.11153 Acta Arith. 192, No. 3, 211-233 (2020). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R37 42C15 11R11 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Johnston, Henri; Nickel, Andreas On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture. (English) Zbl 1470.11280 Math. Z. 292, No. 3-4, 1233-1267 (2019). Reviewer: Gabriel D. Villa Salvador (Ciudad de México) MSC: 11R23 11M41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kashio, Tomokazu On the ratios of Barnes’ multiple gamma functions to the \(p\)-adic analogues. (English) Zbl 1442.11158 J. Number Theory 199, 403-435 (2019). MSC: 11R80 11R27 11R42 11S40 11S80 33B15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mcgown, Kevin J.; Sands, Jonathan W.; Vallières, Daniel Numerical evidence for higher order Stark-type conjectures. (English) Zbl 1458.11161 Math. Comput. 88, No. 315, 389-420 (2019). MSC: 11R42 11R27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dasgupta, Samit; Kakde, Mahesh; Ventullo, Kevin On the Gross-Stark conjecture. (English) Zbl 1416.11160 Ann. Math. (2) 188, No. 3, 833-870 (2018). Reviewer: J. G. M. Mars (Utrecht) MSC: 11R42 11R80 11F41 11F80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Burns, David; Livingstone Boomla, Alice On Selmer groups and refined Stark conjectures. (English) Zbl 1457.11156 Bull. Lond. Math. Soc. 50, No. 5, 845-862 (2018). MSC: 11R42 11R27 11R23 × Cite Format Result Cite Review PDF Full Text: DOI
Livingstone Boomla, Alice On zeta elements and refined abelian Stark conjectures. (English) Zbl 1428.11199 Tokyo J. Math. 40, No. 1, 123-151 (2017). MSC: 11R42 11R23 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Assim, Jilali; Mazigh, Youness; Oukhaba, Hassan Iwasawa theory of Stark units and class groups. (Théorie d’Iwasawa des unités de Stark et groupe de classes.) (French. English summary) Zbl 1428.11192 Int. J. Number Theory 13, No. 5, 1165-1190 (2017). MSC: 11R23 11R27 11R29 11R42 × Cite Format Result Cite Review PDF Full Text: DOI
Tate, John Mazur, Barry (ed.); Serre, Jean-Pierre (ed.) Collected works of John Tate. Part II (1976–2006). Edited by Barry Mazur and Jean-Pierre Serre. (English) Zbl 1386.11002 Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-9093-6/hbk; 978-1-4704-3023-8/ebook). xxv, 751 p. (2016). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-03 14-03 01A75 11Gxx 14Gxx 14Kxx × Cite Format Result Cite Review PDF
Burns, David; Kurihara, Masato; Sano, Takamichi On zeta elements for \(\mathbb G_m\). (English) Zbl 1407.11133 Doc. Math. 21, 555-626 (2016). MSC: 11R42 11R23 11R29 × Cite Format Result Cite Review PDF Full Text: arXiv EMIS
Mazur, Barry; Rubin, Karl Refined class number formulas for \(\mathbb{G}_m\). (English. French summary) Zbl 1414.11155 J. Théor. Nombres Bordx. 28, No. 1, 185-211 (2016). MSC: 11R42 11R27 11R23 11R29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Duke, W.; Li, Y. Harmonic Maass forms of weight 1. (English) Zbl 1414.11057 Duke Math. J. 164, No. 1, 39-113 (2015). Reviewer: Zhengyu Mao (Newark) MSC: 11F37 11F30 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Kashio, Tomokazu A survey on Stark’s conjectures and a result of Dasgupta-Darmon-Pollack. (English) Zbl 1365.11120 RIMS Kôkyûroku Bessatsu B51, 229-268 (2014). MSC: 11R23 11R27 11R42 11M35 11-02 × Cite Format Result Cite Review PDF
Sano, Takamichi Refined abelian Stark conjectures and the equivariant leading term conjecture of Burns. (English) Zbl 1311.11108 Compos. Math. 150, No. 11, 1809-1835 (2014). Reviewer: Andreas Nickel (Bielefeld) MSC: 11R42 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Buckingham, Paul The equivalence of Rubin’s conjecture and the ETNC/LRNC for certain biquadratic extensions. (English) Zbl 1296.11147 Glasg. Math. J. 56, No. 2, 335-353 (2014). Reviewer: Andreas Nickel (Bielefeld) MSC: 11R42 11R27 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
Macias Castillo, Daniel On higher order Stickelberger-type theorems. (English) Zbl 1300.11116 J. Number Theory 133, No. 9, 3007-3032 (2013). Reviewer: Andreas Nickel (Bielefeld) MSC: 11R42 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
Oukhaba, Hassan; Viguié, Stéphane On the Gras conjecture for imaginary quadratic fields. (English) Zbl 1286.11178 Can. Math. Bull. 56, No. 1, 148-160 (2013). Reviewer: Gabriel D. Villa-Salvador (México D. F.) MSC: 11R27 11G16 11R29 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dasgupta, Samit A conjectural product formula for Brumer-Stark units over real quadratic fields. (English) Zbl 1275.11140 J. Number Theory 133, No. 3, 915-925 (2013). Reviewer: Paul Buckingham (Edmonton) MSC: 11R11 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Vallières, Daniel On a generalization of the rank one Rubin-Stark conjecture. (English) Zbl 1368.11117 J. Number Theory 132, No. 11, 2535-2567 (2012). MSC: 11R42 11R29 × Cite Format Result Cite Review PDF Full Text: DOI Link
Macias Castillo, Daniel On higher-order Stickelberger-type theorems for multi-quadratic extensions. (English) Zbl 1300.11115 Int. J. Number Theory 8, No. 1, 95-110 (2012). Reviewer: Andreas Nickel (Bielefeld) MSC: 11R42 11R29 11R11 × Cite Format Result Cite Review PDF Full Text: DOI
Stark, Harold The origin of the “Stark conjectures”. (English) Zbl 1263.11100 Popescu, Cristian (ed.) et al., Arithmetic of \(L\)-functions. Lecture notes from the IAS/Park City Mathematics Institute (PCMI) graduate summer school, Park City, UT, USA, 2009. Providence, RI: American Mathematical Society (AMS); Princeton, NJ: Institute for Advanced Study. (ISBN 978-0-8218-5320-7/hbk). IAS/Park City Mathematics Series 18, 33-44 (2011). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R42 01A60 11-03 11M41 11R11 11R29 × Cite Format Result Cite Review PDF
Tate, John Stark’s basic conjecture. (English) Zbl 1263.11101 Popescu, Cristian (ed.) et al., Arithmetic of \(L\)-functions. Lecture notes from the IAS/Park City Mathematics Institute (PCMI) graduate summer school, Park City, UT, USA, 2009. Providence, RI: American Mathematical Society (AMS); Princeton, NJ: Institute for Advanced Study. (ISBN 978-0-8218-5320-7/hbk). IAS/Park City Mathematics Series 18, 7-31 (2011). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R42 11R27 × Cite Format Result Cite Review PDF
Burns, David On derivatives of Artin \(L\)-series. (English) Zbl 1239.11128 Invent. Math. 186, No. 2, 291-371 (2011). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R42 11R33 11R29 × Cite Format Result Cite Review PDF Full Text: DOI
Dasgupta, Samit; Darmon, Henri; Pollack, Robert Hilbert modular forms and the Gross-Stark conjecture. (English) Zbl 1250.11099 Ann. Math. (2) 174, No. 1, 439-484 (2011). Reviewer: David Loeffler (Coventry) MSC: 11R42 11F41 11F85 × Cite Format Result Cite Review PDF Full Text: DOI
Chapdelaine, Hugo Computation of \(p\)-units in ray class fields of real quadratic number fields. (English) Zbl 1205.11121 Math. Comput. 78, No. 268, 2307-2345 (2009). Reviewer: Andreas Nickel (Regensburg) MSC: 11R42 11Y40 11M36 11R37 11S40 11S80 × Cite Format Result Cite Review PDF Full Text: DOI
Büyükboduk, Kâzım Stark units and the main conjectures for totally real fields. (English) Zbl 1256.11060 Compos. Math. 145, No. 5, 1163-1195 (2009). Reviewer: Filippo Nuccio (Osaka) MSC: 11R23 11R27 11R29 11R42 11R34 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Erickson, Stefan An extension of the first-order Stark conjecture. (English) Zbl 1183.11071 Rocky Mt. J. Math. 39, No. 3, 765-787 (2009). Reviewer: Tauno Metsänkylä (Turku) MSC: 11R42 11R18 11R20 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Chapdelaine, Hugo \(p\)-units in ray class fields of real quadratic number fields. (English) Zbl 1166.11045 Compos. Math. 145, No. 2, 364-392 (2009). Reviewer: Florin Nicolae (Berlin) MSC: 11S40 11R37 11R11 × Cite Format Result Cite Review PDF Full Text: DOI
Charollois, Pierre; Darmon, Henri Arguments for the Stark units and periods of Eisenstein series. (Arguments des unités de Stark et périodes de séries d’Eisenstein.) (French. English summary) Zbl 1206.11062 Algebra Number Theory 2, No. 6, 655-688 (2008). Reviewer: Gerald Gotsbacher (Toronto) MSC: 11F67 11F75 11R42 11M35 11S40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Burns, David On refined Stark conjectures in the non-abelian case. (English) Zbl 1184.11049 Math. Res. Lett. 15, No. 5-6, 841-856 (2008). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R42 11R33 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Manin, Yu. I. Real multiplication and noncommutative geometry (ein Alterstraum). (English) Zbl 1091.11022 Laudal, Olav Arnfinn (ed.) et al., The legacy of Niels Henrik Abel. Papers from the Abel bicentennial conference, University of Oslo, Oslo, Norway, June 3–8, 2002. Berlin: Springer (ISBN 3-540-43826-2/hbk). 685-727 (2004). Reviewer: Florin P. Boca (Urbana-Champaign) MSC: 11M55 11G15 58B34 11R37 11R42 46L89 × Cite Format Result Cite Review PDF
Solomon, David Abelian conjectures of Stark type in \(\mathbb Z_p\)-extensions of totally real fields. (English) Zbl 1065.11092 Burns, David (ed.) et al., Stark’s conjectures: recent work and new directions. Papers from the international conference on Stark’s conjectures and related topics, Johns Hopkins University, Baltimore, MD, USA, August 5–9, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3480-0/pbk). Contemporary Mathematics 358, 143-178 (2004). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R42 11R23 11S40 × Cite Format Result Cite Review PDF Full Text: arXiv
Jehanne, Arnaud; Roblot, Xavier-Francois; Sands, Jonathan Numerical verification of the Stark-Chinburg conjecture for some icosahedral representations. (English) Zbl 1082.11082 Exp. Math. 12, No. 4, 419-432 (2003). Reviewer: Michael Pohst (Berlin) MSC: 11Y40 11R42 × Cite Format Result Cite Review PDF Full Text: DOI EuDML HAL
Stopple, Jeffrey Stark conjectures for CM elliptic curves over number fields. (English) Zbl 1102.11033 J. Number Theory 103, No. 2, 163-196 (2003). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 11G40 11G55 11G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Darmon, Henri; Green, Peter Elliptic curves and class fields of real quadratic fields: Algorithms and evidence. (English) Zbl 1040.11048 Exp. Math. 11, No. 1, 37-55 (2002). MSC: 11G40 11F67 11G05 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Solomon, David Twisted zeta-functions and Abelian Stark conjectures. (English) Zbl 1032.11051 J. Number Theory 94, No. 1, 10-48 (2002). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R42 11R33 × Cite Format Result Cite Review PDF Full Text: DOI
Popescu, Cristian D. Base change for Stark-type conjectures “over \({\mathbb Z}\)”. (English) Zbl 1074.11062 J. Reine Angew. Math. 542, 85-111 (2002). Reviewer: Florin Nicolae (Berlin) MSC: 11R42 11R27 11R33 × Cite Format Result Cite Review PDF Full Text: DOI
Sands, Jonathan W. Stark’s question and Popescu’s conjecture for abelian \(L\)-functions. (English) Zbl 1065.11091 Jutila, Matti (ed.) et al., Number theory. Proceedings of the Turku symposium on number theory in memory of Kustaa Inkeri, Turku, Finland, May 31–June 4, 1999. Berlin: de Gruyter (ISBN 3-11-016481-7/hbk). 305-315 (2001). Reviewer: Tauno Metsänkylä (Turku) MSC: 11R42 11R27 × Cite Format Result Cite Review PDF
Ritter, Jürgen \(L\)-values at zero and the Galois structure of global units. (English) Zbl 0929.11053 Passi, I. B. S. (ed.), Algebra. Some recent advances. Basel: Birkhäuser. Trends in Mathematics. 135-169 (1999). Reviewer: C.Greither (Neubiberg) MSC: 11R42 11R27 11R33 19A31 19B28 11-02 × Cite Format Result Cite Review PDF
Colmez, Pierre \(p\)-adic zeta functions at \(s=0\). (Fonctions zêta \(p\)-adiques en \(s=0\).) (French) Zbl 0864.11062 J. Reine Angew. Math. 467, 89-107 (1995). Reviewer: A.Dabrowski (Szczecin) MSC: 11S40 11R42 × Cite Format Result Cite Review PDF Full Text: DOI Crelle EuDML
Bae, Sunghan Values of \(L\)-functions at \(s = 0\). (English) Zbl 0768.11046 Arch. Math. 58, No. 6, 551-560 (1992). Reviewer: T.Nguyen Quang Do (Besançon) MSC: 11R42 11R34 14G10 × Cite Format Result Cite Review PDF Full Text: DOI
Chinburg, Ted The analytic theory of multiplicative Galois structure. (English) Zbl 0676.12002 Mem. Am. Math. Soc. 395, 158 p. (1989). Reviewer: George Gras MSC: 11R33 11R27 11R23 11R37 11R42 11R34 11-04 11S40 × Cite Format Result Cite Review PDF Full Text: DOI
Sands, Jonathan W. Stark’s conjecture and Abelian \(L\)-functions with higher order zeros at \(s=0\). (English) Zbl 0631.12006 Adv. Math. 66, 62-87 (1987). Reviewer: Georges Gras (Besançon) MSC: 11R42 11R18 × Cite Format Result Cite Review PDF Full Text: DOI
Gekeler, E.-U. Satake compactification of Drinfeld modular schemes. (English) Zbl 0657.14012 p-adic analysis, Proc. Conf., Houthalen/Belg. 1986, 71-81 (1986). Reviewer: E.U.Gekeler MSC: 14G25 11F06 11R58 11F27 14L05 14G10 × Cite Format Result Cite Review PDF
Arakawa, Tsuneo On the Stark-Shintani conjecture and certain relative class numbers. (English) Zbl 0615.12015 Automorphic forms and number theory, Proc. Symp., Sendai/Jap. 1983, Adv. Stud. Pure Math. 7, 1-6 (1985). Reviewer: G.Gras MSC: 11R42 11R23 × Cite Format Result Cite Review PDF
Hayes, David R. Stickelberger elements in function fields. (English) Zbl 0569.12008 Compos. Math. 55, 209-239 (1985). Reviewer: David Goss (Columbus/Ohio) MSC: 11R60 11R23 11R42 11G09 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML
Nakagawa, Jin On the Stark-Shintani conjecture and cyclotomic \({\mathbb{Z}}_ p\)-extensions of class fields over real quadratic fields. II. (English) Zbl 0549.12009 Tohoku Math. J., II. Ser. 36, 439-452 (1984). Reviewer: G.Gras MSC: 11R42 11R11 11R18 11R27 11M06 × Cite Format Result Cite Review PDF Full Text: DOI
Nakagawa, Jin On the Stark-Shintani conjecture and cyclotomic \({\mathbb{Z}}_ p\)-extensions of class fields over real quadratic fields. (English) Zbl 0549.12008 J. Math. Soc. Japan 36, 577-588 (1984). Reviewer: G.Gras MSC: 11R42 11R11 11R18 11M06 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Stark, H. M. The Coates-Wiles theorem revisited. (English) Zbl 0542.14010 Number theory related to Fermat’s last theorem, Proc. Conf., Prog. Math. 26, 349-362 (1982). Reviewer: H.G.Zimmer MSC: 14G10 14H25 11R18 11R37 14G25 × Cite Format Result Cite Review PDF
Gross, Benedict H. p-adic L-series at s=0. (English) Zbl 0507.12010 J. Fac. Sci., Univ. Tokyo, Sect. I A 28, 979-994 (1981). MSC: 11S40 11R80 11R37 × Cite Format Result Cite Review PDF