Lemmermeyer, Franz David Hilbert: The theory of algebraic number fields. Jahresber. Deutsche Math. Ver. 4 (1897), 175–546. (David Hilbert: Die Theorie der algebraischen Zahlkörper. Jahresber. Deutsche Math. Ver. 4 (1897), 175–546.) (English) Zbl 1397.01016 Jahresber. Dtsch. Math.-Ver. 120, No. 1, 41-79 (2018). Reviewer: Stefan Neuwirth (Besançon) MSC: 01A55 01A60 11-03 11A15 11R04 PDF BibTeX XML Cite \textit{F. Lemmermeyer}, Jahresber. Dtsch. Math.-Ver. 120, No. 1, 41--79 (2018; Zbl 1397.01016) Full Text: DOI OpenURL
de Boer, Koen; Pagano, Carlo Calculating the power residue symbol and ibeta. Applications of computing the group structure of the principal units of a \(\mathfrak{p}\)-adic number field completion. (English) Zbl 1472.11317 Burr, Michael (ed.), Proceedings of the 42nd international symposium on symbolic and algebraic computation, ISSAC 2017, Kaiserslautern, Germany, July 25–28, 2017. New York, NY: Association for Computing Machinery (ACM). 117-124 (2017). MSC: 11Y16 11Y40 68W30 PDF BibTeX XML Cite \textit{K. de Boer} and \textit{C. Pagano}, in: Proceedings of the 42nd international symposium on symbolic and algebraic computation, ISSAC 2017, Kaiserslautern, Germany, July 25--28, 2017. New York, NY: Association for Computing Machinery (ACM). 117--124 (2017; Zbl 1472.11317) Full Text: DOI OpenURL
Sivatski, A. S. Central simple algebras of prime exponent and divided power operations. (English) Zbl 1275.16020 J. \(K\)-Theory 11, No. 1, 113-123 (2013). Reviewer: Ivan D. Chipchakov (Sofia) MSC: 16K50 19D45 16K20 PDF BibTeX XML Cite \textit{A. S. Sivatski}, J. \(K\)-Theory 11, No. 1, 113--123 (2013; Zbl 1275.16020) Full Text: DOI Link OpenURL
Vostokov, S. V.; Ivanov, M. A. The Eisenstein reciprocity law for formal Lubin-Tate groups. (English. Russian original) Zbl 1300.11121 J. Math. Sci., New York 180, No. 3, 269-277 (2012); translation from Zap. Nauchn. Semin. POMI 386, 129-143 (2011). MSC: 11S31 PDF BibTeX XML Cite \textit{S. V. Vostokov} and \textit{M. A. Ivanov}, J. Math. Sci., New York 180, No. 3, 269--277 (2012; Zbl 1300.11121); translation from Zap. Nauchn. Semin. POMI 386, 129--143 (2011) Full Text: DOI OpenURL
Caranay, Perlas C.; Scheidler, Renate An efficient seventh power residue symbol algorithm. (English) Zbl 1242.11079 Int. J. Number Theory 6, No. 8, 1831-1853 (2010). Reviewer: Preda Mihailescu (Göttingen) MSC: 11R18 11A15 11A05 11Y16 PDF BibTeX XML Cite \textit{P. C. Caranay} and \textit{R. Scheidler}, Int. J. Number Theory 6, No. 8, 1831--1853 (2010; Zbl 1242.11079) Full Text: DOI OpenURL
Frei, Günther Developments in the theory of algebras over number fields: a new foundation for the Hasse norm residue symbol and new approaches to both the Artin reciprocity law and class field theory. (English) Zbl 1151.01009 Gray, Jeremy J. (ed.) et al., Episodes in the history of modern algebra (1800–1950). Based on a workshop held at MSRI, Berkeley, CA, USA, April 2003. Providence, RI: American Mathematical Society (AMS); London: London Mathematical Society (ISBN 978-0-8218-4343-7/hbk). History of Mathematics 32, 117-151 (2007). Reviewer: Ülo Lumiste (Tartu) MSC: 01A55 01A60 11-03 PDF BibTeX XML Cite \textit{G. Frei}, in: Episodes in the history of modern algebra (1800--1950). Based on a workshop held at MSRI, Berkeley, CA, USA, April 2003. Providence, RI: American Mathematical Society (AMS); London: London Mathematical Society. 117--151 (2007; Zbl 1151.01009) OpenURL
Fenster, Della D.; Schwermer, Joachim Beyond class field theory: Helmut Hasse’s arithmetic in the theory of algebras in early 1931. (English) Zbl 1128.01022 Arch. Hist. Exact Sci. 61, No. 5, 425-456 (2007). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 01A60 PDF BibTeX XML Cite \textit{D. D. Fenster} and \textit{J. Schwermer}, Arch. Hist. Exact Sci. 61, No. 5, 425--456 (2007; Zbl 1128.01022) Full Text: DOI OpenURL
Merkurjev, Alexander On the norm residue homomorphism of degree two. (English) Zbl 1180.19001 Uraltseva, N.N.(ed.), Proceedings of the St. Petersburg Mathematical Society. Vol. XII. Transl. from the Russian. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-4205-6/hbk). Transl., Ser. 2, Am. Math. Soc. 219, 103-124 (2006). MSC: 19C30 14F43 16K50 PDF BibTeX XML Cite \textit{A. Merkurjev}, Transl., Ser. 2, Am. Math. Soc. 219, 103--124 (2006; Zbl 1180.19001) OpenURL
Azizi, Abdelmalek; Mouhib, Ali The 2-rank of the class group of certain biquadratic fields and applications. (Le 2-rang du groupe de classes de certains corps biquadratiques et applications.) (French) Zbl 1051.11057 Int. J. Math. 15, No. 2, 169-182 (2004). Reviewer: Elliot Benjamin (Swanville) MSC: 11R29 11R27 11R37 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{A. Mouhib}, Int. J. Math. 15, No. 2, 169--182 (2004; Zbl 1051.11057) Full Text: DOI OpenURL
Ichimura, Humio Note on cyclotomic units and Gauss sums in local cyclotomic fields. (English) Zbl 0988.11053 J. Number Theory 90, No. 1, 154-165 (2001). Reviewer: Lawrence Washington (College Park) MSC: 11R18 11R23 11R37 11L05 PDF BibTeX XML Cite \textit{H. Ichimura}, J. Number Theory 90, No. 1, 154--165 (2001; Zbl 0988.11053) Full Text: DOI OpenURL
Azizi, Abdelmalek; Mouhib, Ali On the rank of the \(2\)-class group of \(\mathbb{Q}(\sqrt m,\sqrt d)\) where \(m=2\) or a prime \(p\equiv 1\pmod 4\). (Sur le rang du \(2\)-groupe de classes de \(\mathbb{Q}({\sqrt{m}},{\sqrt{d}})\) où \(m=2\) ou un premier \(p\equiv 1\pmod 4\).) (English) Zbl 0986.11073 Trans. Am. Math. Soc. 353, No. 7, 2741-2752 (2001). Reviewer: E.Benjamin (Belfast / Maine) MSC: 11R29 11R16 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{A. Mouhib}, Trans. Am. Math. Soc. 353, No. 7, 2741--2752 (2001; Zbl 0986.11073) Full Text: DOI OpenURL
Sharifi, Romyar T. On norm residue symbols and conductors. (English) Zbl 0970.11042 J. Number Theory 86, No. 2, 196-209 (2001). Reviewer: Abbas Movahhedi (Limoges) MSC: 11S15 11S99 PDF BibTeX XML Cite \textit{R. T. Sharifi}, J. Number Theory 86, No. 2, 196--209 (2001; Zbl 0970.11042) Full Text: DOI Link OpenURL
Kubota, Tomio; Oka, Satomi On the deduction of the class field theory from the general reciprocity of power residues. (English) Zbl 0967.11047 Nagoya Math. J. 160, 135-142 (2000). Reviewer: Satomi Oka (Nagoya) MSC: 11R37 11E12 PDF BibTeX XML Cite \textit{T. Kubota} and \textit{S. Oka}, Nagoya Math. J. 160, 135--142 (2000; Zbl 0967.11047) Full Text: DOI OpenURL
Colliot-Thélène, Jean-Louis Galois cohomology of Henselian discrete valuation fields, after K. Kato and S. Bloch. (Cohomologie galoisienne des corps valués discrets henseliens, d’après K. Kato et S. Bloch.) (French) Zbl 0976.11053 Bass, H. (ed.) et al., Algebraic \(K\)-theory and its applications. Proceedings of the workshop and symposium, ICTP, Trieste, Italy, September 1-19, 1997. Singapore: World Scientific. 120-163 (1999). Reviewer: I.Fesenko (Nottingham) MSC: 11S25 19D45 11S31 14F30 19F15 PDF BibTeX XML Cite \textit{J.-L. Colliot-Thélène}, in: Algebraic \(K\)-theory and its applications. Proceedings of the workshop and symposium, ICTP, Trieste, Italy, September 1--19, 1997. Singapore: World Scientific. 120--163 (1999; Zbl 0976.11053) OpenURL
Gras, Georges; Cortella, Anne Interpretation and calculation of the defect group of the Hasse principle. (Interprétation et calcul du groupe de défaut d’un principe de Hasse.) (French) Zbl 0897.11034 Math. Nachr. 188, 109-140 (1997). Reviewer: H.G.Quebbemann (Oldenburg) MSC: 11R37 11E39 11R32 PDF BibTeX XML Cite \textit{G. Gras} and \textit{A. Cortella}, Math. Nachr. 188, 109--140 (1997; Zbl 0897.11034) Full Text: DOI OpenURL
Miki, Hiroo Jacobi sums and the Hilbert symbol for a power of two. (English) Zbl 0895.11042 J. Math. Soc. Japan 48, No. 2, 367-408 (1996). Reviewer: L.Washington (College Park) MSC: 11R18 11L05 PDF BibTeX XML Cite \textit{H. Miki}, J. Math. Soc. Japan 48, No. 2, 367--408 (1996; Zbl 0895.11042) Full Text: DOI OpenURL
Bell, Robert A. On the properties of the Vostokov and Parshin pairing in higher local class field theory. (English) Zbl 0864.11061 J. Pure Appl. Algebra 108, No. 1, 7-16 (1996). Reviewer: Zhang Xianke (Beijing) MSC: 11S31 PDF BibTeX XML Cite \textit{R. A. Bell}, J. Pure Appl. Algebra 108, No. 1, 7--16 (1996; Zbl 0864.11061) Full Text: DOI OpenURL
Bell, Robert A. On properties of the \(n\)-dimensional norm residue symbol in higher local class field theory. (English) Zbl 0864.11060 J. Pure Appl. Algebra 108, No. 1, 1-6 (1996). Reviewer: Zhang Xianke (Beijing) MSC: 11S31 PDF BibTeX XML Cite \textit{R. A. Bell}, J. Pure Appl. Algebra 108, No. 1, 1--6 (1996; Zbl 0864.11060) Full Text: DOI OpenURL
Helou, Charles Norm residue symbol and cyclotomic units. (English) Zbl 0866.11062 Acta Arith. 73, No. 2, 147-188 (1995); corrigendum 98, No. 3, 311 (2001). Reviewer: Franz Lemmermeyer (Heidelberg) MSC: 11R18 11R27 PDF BibTeX XML Cite \textit{C. Helou}, Acta Arith. 73, No. 2, 147--188 (1995; Zbl 0866.11062) Full Text: DOI EuDML OpenURL
Destrempes, François Explicit reciprocity laws for Lubin-Tate modules. (English) Zbl 0821.11059 J. Reine Angew. Math. 463, 27-47 (1995). Reviewer: I.Fesenko (Nottingham) MSC: 11S31 PDF BibTeX XML Cite \textit{F. Destrempes}, J. Reine Angew. Math. 463, 27--47 (1995; Zbl 0821.11059) Full Text: DOI Crelle EuDML OpenURL
Miki, Hiroo On the calculation of certain Hilbert norm residue symbols and its application. (English) Zbl 0829.11053 J. Number Theory 50, No. 1, 87-105 (1995). Reviewer: N.Yui (Kingston/Ontario) MSC: 11R18 11R37 PDF BibTeX XML Cite \textit{H. Miki}, J. Number Theory 50, No. 1, 87--105 (1995; Zbl 0829.11053) Full Text: DOI OpenURL
Kuz’min, L. V. Some explicit calculations in local and global cyclotomic fields. (English. Russian original) Zbl 0877.11055 Proc. Steklov Inst. Math. 208, 179-197 (1995); translation from Tr. Mat. Inst. Steklova 208, 202-222 (1995). Reviewer: F.Lemmermeyer (Heidelberg) MSC: 11R23 11S25 PDF BibTeX XML Cite \textit{L. V. Kuz'min}, in: Number theory, algebra and algebraic geometry. Collected papers. In honor of the seventieth birthday of Academician Igor Rostislavovich Shafarevich. Moscow: Maik Nauka/Interperiodica Publishing. 179--197 (1995; Zbl 0877.11055); translation from Tr. Mat. Inst. Steklova 208, 202--222 (1995) OpenURL
Simons, Lloyd The Galois-equivariant structure of the norm residue symbol in tamely ramified-extensions of 2-adic number fields. (English) Zbl 0816.11062 Math. Nachr. 169, 267-277 (1994). Reviewer: M.Epkenhans (Paderborn) MSC: 11S15 11S20 PDF BibTeX XML Cite \textit{L. Simons}, Math. Nachr. 169, 267--277 (1994; Zbl 0816.11062) Full Text: DOI OpenURL
Stolin, Alexander An explicit formula for the Picard group of the cyclic group of order \(p^ 2\). (English) Zbl 0834.11040 Proc. Am. Math. Soc. 121, No. 2, 375-383 (1994). Reviewer: T.Nguyen Quang Do (Besançon) MSC: 11R18 11R29 19A31 PDF BibTeX XML Cite \textit{A. Stolin}, Proc. Am. Math. Soc. 121, No. 2, 375--383 (1994; Zbl 0834.11040) Full Text: DOI OpenURL
Sueyoshi, Yutaka Explicit reciprocity formulas in 2-adic number fields. (English) Zbl 0806.11056 Tokyo J. Math. 16, No. 2, 355-361 (1993). Reviewer: Zhang Xianke (Beijing) MSC: 11S31 PDF BibTeX XML Cite \textit{Y. Sueyoshi}, Tokyo J. Math. 16, No. 2, 355--361 (1993; Zbl 0806.11056) Full Text: DOI OpenURL
Sury, B. A variant of Moore’s uniqueness of reciprocity laws. (English) Zbl 0790.11077 Mathematika 40, No. 2, 246-255 (1993). Reviewer: S.Sury (Bombay) MSC: 11R37 20G35 20G30 PDF BibTeX XML Cite \textit{B. Sury}, Mathematika 40, No. 2, 246--255 (1993; Zbl 0790.11077) Full Text: DOI OpenURL
Sueyoshi, Yutaka Explicit reciprocity laws on relative Lubin-Tate groups. (English) Zbl 0663.14031 Acta Arith. 55, No. 3, 291-299 (1990). Reviewer: Y.Sueyoshi MSC: 11S31 14L05 11A15 PDF BibTeX XML Cite \textit{Y. Sueyoshi}, Acta Arith. 55, No. 3, 291--299 (1990; Zbl 0663.14031) Full Text: DOI EuDML OpenURL
Hélou, Charles Classical explicit reciprocity. (English) Zbl 0714.11083 Théorie des nombres, C. R. Conf. Int., Québec/Can. 1987, 359-370 (1989). Reviewer: Zhang Xianke MSC: 11S15 11S31 PDF BibTeX XML OpenURL
Vostokov, S. V.; Fesenko, I. B. A certain property of the Hilbert pairing. (English. Russian original) Zbl 0692.14030 Math. Notes 43, No. 3, 226-230 (1988); translation from Mat. Zametki 43, No. 3, 393-400 (1988). Reviewer: Yu. G. Zarhin (Moskva) MSC: 14L05 11S31 PDF BibTeX XML Cite \textit{S. V. Vostokov} and \textit{I. B. Fesenko}, Math. Notes 43, No. 3, 226--230 (1988; Zbl 0692.14030); translation from Mat. Zametki 43, No. 3, 393--400 (1988) Full Text: DOI OpenURL
Riehm, C. The Schur subgroup of the Brauer group of a local field. (English) Zbl 0653.12007 Enseign. Math., II. Sér. 34, No. 1-2, 1-11 (1988). Reviewer: R.A.Mollin MSC: 11S31 14F22 PDF BibTeX XML Cite \textit{C. Riehm}, Enseign. Math. (2) 34, No. 1--2, 1--11 (1988; Zbl 0653.12007) OpenURL
Riehm, C. The Schur subgroup of the Brauer group of a local field. (English) Zbl 0653.00024 Enseign. Math., II. Sér. 34, No. 1-2, 1-11 (1988). Reviewer: Richard A. Mollin (Calgary) MSC: 11S25 11S31 11S20 11S45 14F22 16S32 PDF BibTeX XML Cite \textit{C. Riehm}, Enseign. Math. (2) 34, No. 1--2, 1--11 (1988; Zbl 0653.00024) Full Text: Link OpenURL
Helou, Charles An explicit \(2^ n\)-th reciprocity law. (English) Zbl 0638.12008 J. Reine Angew. Math. 389, 64-89 (1988). Reviewer: C.Helou MSC: 11S85 PDF BibTeX XML Cite \textit{C. Helou}, J. Reine Angew. Math. 389, 64--89 (1988; Zbl 0638.12008) Full Text: DOI Crelle EuDML OpenURL
Vostokov, S. V. The second factor in the reciprocity law. (English) Zbl 0612.12009 J. Sov. Math. 37, 953-958 (1987). MSC: 11S20 PDF BibTeX XML Cite \textit{S. V. Vostokov}, J. Sov. Math. 37, 953--958 (1987; Zbl 0612.12009) Full Text: DOI OpenURL
Simons, Lloyd D. The Hilbert symbol for tamely ramified abelian extensions of 2-adic number fields. (English) Zbl 0608.12019 Manuscr. Math. 58, 345-362 (1987). Reviewer: Lloyd D. Simons MSC: 11S31 11S15 PDF BibTeX XML Cite \textit{L. D. Simons}, Manuscr. Math. 58, 345--362 (1987; Zbl 0608.12019) Full Text: DOI EuDML OpenURL
Merkur’ev, A. S. \(K_2\) of fields and the Brauer group. (English) Zbl 0608.12028 Applications of algebraic K-theory to algebraic geometry and number theory, Proc. AMS-IMS-SIAM Joint Summer Res. Conf., Boulder/Colo. 1983, Part II, Contemp. Math. 55, 529-546 (1986). Reviewer: Manuel Ojanguren (Lausanne) MSC: 19C30 19F15 12G05 18F25 PDF BibTeX XML OpenURL
Vostokov, S. V. Explicit construction of class field theory for a multidimensional local field. (English. Russian original) Zbl 0608.12017 Math. USSR, Izv. 26, 263-287 (1986); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 49, No. 2, 283-308 (1985). Reviewer: A. N. Parshin (Moskva) MSC: 11S31 18F25 19C30 11S70 PDF BibTeX XML Cite \textit{S. V. Vostokov}, Math. USSR, Izv. 26, 263--287 (1986; Zbl 0608.12017); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 49, No. 2, 283--308 (1985) Full Text: DOI OpenURL
de Shalit, Ehud The explicit reciprocity law in local class field theory. (English) Zbl 0597.12018 Duke Math. J. 53, 165-176 (1986). Reviewer: Zhang Xianke MSC: 11S31 14L05 PDF BibTeX XML Cite \textit{E. de Shalit}, Duke Math. J. 53, 165--176 (1986; Zbl 0597.12018) Full Text: DOI OpenURL
Akagawa, Yasumasa A tripling on the algebraic number field. (English) Zbl 0591.12013 Osaka J. Math. 23, 151-179 (1986). Reviewer: T.Takeuchi MSC: 11R37 11R18 11S31 PDF BibTeX XML Cite \textit{Y. Akagawa}, Osaka J. Math. 23, 151--179 (1986; Zbl 0591.12013) OpenURL
Neukirch, Jürgen Class field theory. (English) Zbl 0587.12001 Grundlehren der Mathematischen Wissenschaften, 280. Berlin etc.: Springer-Verlag. VIII, 140 p. DM 84.00 (1986). Reviewer: N.Klingen MSC: 11R37 12-02 11S31 PDF BibTeX XML OpenURL
Prasad, Gopal On the ”wild” norm residue symbol in an abelian extension. (English) Zbl 0576.12017 Math. Ann. 274, 419-422 (1986). MSC: 11S31 11S45 PDF BibTeX XML Cite \textit{G. Prasad}, Math. Ann. 274, 419--422 (1986; Zbl 0576.12017) Full Text: DOI EuDML OpenURL
Rapinchuk, A. S. On the metaplectic kernel for anisotropic groups. (English. Russian original) Zbl 0791.20049 Selected papers in \(K\)-theory. Transl., Ser. 2, Am. Math. Soc. 154, 81-85 (1992); translation from Dokl. Akad. Nauk BSSR 29, 1068-1071 (1985). MSC: 20G30 11R34 16K20 11R52 19B14 PDF BibTeX XML OpenURL
Rapinchuk, A. S. On the metaplectic kernel for anisotropic groups. (Russian. English summary) Zbl 0616.12007 Dokl. Akad. Nauk BSSR 29, 1068-1071 (1985). Reviewer: S.A.Basarab MSC: 11R52 11R34 20G30 PDF BibTeX XML Cite \textit{A. S. Rapinchuk}, Dokl. Akad. Nauk BSSR 29, 1068--1071 (1985; Zbl 0616.12007) OpenURL
Jaulent, Jean-François Sur la formule du produit pour le symbole de reste normique généralisé. (On the product formula for the generalized norm residue symbol). (French) Zbl 0584.12006 Acta Arith. 45, 249-254 (1985). Reviewer: L.G.Roberts MSC: 11R37 11S31 PDF BibTeX XML Cite \textit{J.-F. Jaulent}, Acta Arith. 45, 249--254 (1985; Zbl 0584.12006) Full Text: DOI EuDML OpenURL
Chase, Stephen U. A generalization of the norm residue symbol. (English) Zbl 0576.12016 J. Pure Appl. Algebra 38, 39-63 (1985). Reviewer: L.N.Childs MSC: 11S31 14F22 11S25 13B05 12G05 PDF BibTeX XML Cite \textit{S. U. Chase}, J. Pure Appl. Algebra 38, 39--63 (1985; Zbl 0576.12016) Full Text: DOI OpenURL
Vostokov, S. V. On class field theory of a multidimensional local field. (English. Russian original) Zbl 0608.12018 Sov. Math., Dokl. 29, 87-88 (1984); translation from Dokl. Akad. Nauk SSSR 274, 780-782 (1984). Reviewer: A. N. Parshin (Moskva) MSC: 11S31 11S70 18F25 19C30 PDF BibTeX XML Cite \textit{S. V. Vostokov}, Sov. Math., Dokl. 29, 87--88 (1984; Zbl 0608.12018); translation from Dokl. Akad. Nauk SSSR 274, 780--782 (1984) OpenURL
Shiratani, Katsumi; Ishibashi, Makoto On explicit formulas for the norm residue symbol in prime cyclotomic fields. (English) Zbl 0595.12008 Mem. Fac. Sci., Kyushu Univ., Ser. A 38, 203-231 (1984). Reviewer: J.V.Armitage MSC: 11S31 11R37 11T22 PDF BibTeX XML Cite \textit{K. Shiratani} and \textit{M. Ishibashi}, Mem. Fac. Sci., Kyushu Univ., Ser. A 38, 203--231 (1984; Zbl 0595.12008) Full Text: DOI OpenURL
Prasad, Gopal; Raghunathan, M. S. Topological central extensions of semi-simple groups over local fields. I, II. (English) Zbl 0552.20025 Ann. Math. (2) 119, 143-201, 203-268 (1984). Reviewer: P.Gérardin MSC: 20G25 14L15 20G10 22E20 14E20 PDF BibTeX XML Cite \textit{G. Prasad} and \textit{M. S. Raghunathan}, Ann. Math. (2) 119, 143--201, 203--268 (1984; Zbl 0552.20025) Full Text: DOI OpenURL
Iwasawa, Kenkichi Local class field theory. Transl. from the Japanese by A. A. Bel’skiĭ. Transl. ed. by B. B. Venkov. (Локалная теория полей классов.) (Russian) Zbl 0566.12005 Moskva: Izdatel’stvo ”Mir”. 184 pp. R. 1.40 (1983). MSC: 11S31 11-02 11S25 11S15 14F22 12G05 PDF BibTeX XML OpenURL
Vostokov, S. V. Hilbert symbol in a discrete valuated field. (English) Zbl 0486.12007 J. Sov. Math. 19, 1006-1019 (1982). MSC: 11S85 11R27 12J10 PDF BibTeX XML Cite \textit{S. V. Vostokov}, J. Sov. Math. 19, 1006--1019 (1982; Zbl 0486.12007) Full Text: DOI OpenURL
Bloch, Spencer Algebraic K-theory and classfield theory for arithmetic surfaces. (English) Zbl 0512.14009 Ann. Math. (2) 114, 229-265 (1981). MSC: 14C35 14H25 11R37 14H30 11R70 PDF BibTeX XML Cite \textit{S. Bloch}, Ann. Math. (2) 114, 229--265 (1981; Zbl 0512.14009) Full Text: DOI OpenURL
Coleman, Robert F. The dilogarithm and the norm residue symbol. (English) Zbl 0493.12019 Bull. Soc. Math. Fr. 109, 373-402 (1981). MSC: 11S15 11S80 PDF BibTeX XML Cite \textit{R. F. Coleman}, Bull. Soc. Math. Fr. 109, 373--402 (1981; Zbl 0493.12019) Full Text: DOI Numdam EuDML OpenURL
Vostokov, S. V. Symbols on formal groups. (Russian) Zbl 0483.14011 Izv. Akad. Nauk SSSR, Ser. Mat. 45, 985-1014 (1981). Reviewer: S. V. Vostokov MSC: 11S31 11S70 14L05 19F15 PDF BibTeX XML Cite \textit{S. V. Vostokov}, Izv. Akad. Nauk SSSR, Ser. Mat. 45, 985--1014 (1981; Zbl 0483.14011) Full Text: MNR OpenURL
Coleman, Robert F. The arithmetic of Lubin-Tate division towers. (English) Zbl 0475.12021 Duke Math. J. 48, 449-466 (1981). MSC: 11S31 14L05 11S15 11R18 PDF BibTeX XML Cite \textit{R. F. Coleman}, Duke Math. J. 48, 449--466 (1981; Zbl 0475.12021) Full Text: DOI OpenURL
Hamada, Suguru On the conductors of p-cyclic Kummer extensions of local number fields. (English) Zbl 0505.12019 Kodai Math. J. 3, 415-428 (1980). MSC: 11S15 PDF BibTeX XML Cite \textit{S. Hamada}, Kodai Math. J. 3, 415--428 (1980; Zbl 0505.12019) Full Text: DOI OpenURL
Vostokov, S. V. A norm pairing in formal modules. (English. Russian original) Zbl 0463.12008 Math. USSR, Izv. 15, 25-51 (1980); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 43, 765-794 (1979). Reviewer: G. Angermüller MSC: 11S31 14L05 PDF BibTeX XML Cite \textit{S. V. Vostokov}, Math. USSR, Izv. 15, 25--51 (1980; Zbl 0463.12008); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 43, 765--794 (1979) Full Text: DOI OpenURL
Kolyvagin, V. A. Formal groups and the norm residue symbol. (English) Zbl 0443.12005 Math. USSR, Izv. 15, 289-348 (1980). MSC: 11S31 14L05 11S15 PDF BibTeX XML Cite \textit{V. A. Kolyvagin}, Math. USSR, Izv. 15, 289--348 (1980; Zbl 0443.12005) Full Text: DOI OpenURL
Sen, Shankar On explicit reciprocity laws. (English) Zbl 0411.12005 J. Reine Angew. Math. 313, 1-26 (1980). MSC: 11S31 11A15 PDF BibTeX XML Cite \textit{S. Sen}, J. Reine Angew. Math. 313, 1--26 (1980; Zbl 0411.12005) Full Text: DOI Crelle EuDML Link OpenURL
Vostokov, S. V. Explicit form of the law of reciprocity. (English) Zbl 0467.12018 Math. USSR, Izv. 13, 557-588 (1979). MSC: 11S31 11R37 11S15 PDF BibTeX XML Cite \textit{S. V. Vostokov}, Math. USSR, Izv. 13, 557--588 (1979; Zbl 0467.12018) Full Text: DOI OpenURL
Coleman, Robert F. Division values in local fields. (English) Zbl 0429.12010 Invent. Math. 53, 91-116 (1979). MSC: 11S31 14L05 PDF BibTeX XML Cite \textit{R. F. Coleman}, Invent. Math. 53, 91--116 (1979; Zbl 0429.12010) Full Text: DOI EuDML OpenURL
Kolyvagin, V. A. Formal groups and the norm residue symbol. (Russian) Zbl 0429.12009 Izv. Akad. Nauk SSSR, Ser. Mat. 43, 1054-1120 (1979). MSC: 11S31 14L05 PDF BibTeX XML Cite \textit{V. A. Kolyvagin}, Izv. Akad. Nauk SSSR, Ser. Mat. 43, 1054--1120 (1979; Zbl 0429.12009) OpenURL
Vostokov, S. V. On the law of reciprocity in an algebraic number field. (English. Russian original) Zbl 0464.12007 Proc. Steklov Inst. Math. 148, 75-79 (1980); translation from Tr. Mat. Inst. Steklova 148, 77-81 (1978). MSC: 11S99 11R27 PDF BibTeX XML Cite \textit{S. V. Vostokov}, Proc. Steklov Inst. Math. 148, 75--79 (1978; Zbl 0464.12007); translation from Tr. Mat. Inst. Steklova 148, 77--81 (1978) OpenURL
Vostokov, S. V. The second factor in the reciprocity law. (Russian) Zbl 0449.12004 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 75, 59-66 (1978). MSC: 11S20 PDF BibTeX XML Cite \textit{S. V. Vostokov}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 75, 59--66 (1978; Zbl 0449.12004) Full Text: EuDML OpenURL
Kolyvagin, V. A. The norm residue symbol in local fields. (English. Russian original) Zbl 0424.12011 Russ. Math. Surv. 33, No. 6, 239-240 (1978); translation from Usp. Mat. Nauk 33, No. 6(204), 217-218 (1978). MSC: 11S31 PDF BibTeX XML Cite \textit{V. A. Kolyvagin}, Russ. Math. Surv. 33, No. 6, 239--240 (1978; Zbl 0424.12011); translation from Usp. Mat. Nauk 33, No. 6(204), 217--218 (1978) Full Text: DOI OpenURL
Vostokov, S. V. Eine explizite Form des Reziprozitätsgesetzes. (Russian) Zbl 0408.12002 Izv. Akad. Nauk SSSR, Ser. Mat. 42, 1288-1321 (1978). MSC: 11R04 11R37 PDF BibTeX XML Cite \textit{S. V. Vostokov}, Izv. Akad. Nauk SSSR, Ser. Mat. 42, 1288--1321 (1978; Zbl 0408.12002) OpenURL
Vostokov, S. V. On the explicit form of the reciprocity law. (English. Russian original) Zbl 0393.12001 Sov. Math., Dokl. 19, 198-201 (1978); translation from Dokl. Akad. Nauk SSSR 238, 1276-1278 (1978). Reviewer: Hideo Yokoi (Aichi) MSC: 11S31 PDF BibTeX XML Cite \textit{S. V. Vostokov}, Sov. Math., Dokl. 19, 198--201 (1978; Zbl 0393.12001); translation from Dokl. Akad. Nauk SSSR 238, 1276--1278 (1978) OpenURL
van der Kallen, Wilberd The \(K_2\) of rings with many units. (English) Zbl 0393.18012 Ann. Sci. Éc. Norm. Supér. (4) 10, 473-515 (1977). MSC: 18F25 13D15 PDF BibTeX XML Cite \textit{W. van der Kallen}, Ann. Sci. Éc. Norm. Supér. (4) 10, 473--515 (1977; Zbl 0393.18012) Full Text: DOI Numdam EuDML OpenURL
Coates, J.; Wiles, A. Explicit reciprocity laws. (English) Zbl 0358.12001 Astérisque 41-42, 7-17 (1977). Reviewer: Gr. Todorova MSC: 11S31 PDF BibTeX XML Cite \textit{J. Coates} and \textit{A. Wiles}, Astérisque 41--42, 7--17 (1977; Zbl 0358.12001) OpenURL
Serre, Jean-Pierre A course in arithmetic. (Cours d’arithmétique.) (French) Zbl 0225.12002 Le mathématicien. 2. Paris: Presses Universitaires de France. 188 p. (1970). Reviewer: Gottfried Bruckner (Berlin) MSC: 11-01 11E04 11E08 11E25 11E39 11E45 11F11 11F27 11N13 11Rxx 11Sxx PDF BibTeX XML OpenURL
Artin, Emil; Tate, John Class field theory. (English) Zbl 0176.33504 New York-Amsterdam: W. A. Benjamin, Inc., xxvi, 259 pp. (1968). Reviewer: Gottfried Bruckner (Berlin) MSC: 11R37 11-02 11R34 11S15 11S31 01A75 PDF BibTeX XML OpenURL
Lubin, Jonathan; Tate, John Formal complex multiplication in local fields. (English) Zbl 0128.26501 Ann. Math. (2) 81, 380-387 (1965). Reviewer: H. Brückner MSC: 11S15 11G15 12J99 PDF BibTeX XML Cite \textit{J. Lubin} and \textit{J. Tate}, Ann. Math. (2) 81, 380--387 (1965; Zbl 0128.26501) Full Text: DOI Link OpenURL
Shafarevich, I. R. A general reciprocity law. (Russian) Zbl 0036.15901 Mat. Sb., N. Ser. 26(68), 113-146 (1950). Reviewer: Helmut Hasse (Hamburg) MSC: 11R18 11A15 PDF BibTeX XML Cite \textit{I. R. Shafarevich}, Mat. Sb., Nov. Ser. 26(68), 113--146 (1950; Zbl 0036.15901) Full Text: MNR OpenURL
Shafarevich, I. R. A general reciprocity law. (Das allgemeine Reziprozitätsgesetz.) (Russian) Zbl 0032.39201 Dokl. Akad. Nauk SSSR, n. Ser. 64, 25-28 (1949). Reviewer: Helmut Hasse (Berlin) MSC: 11R37 11R18 PDF BibTeX XML Cite \textit{I. R. Shafarevich}, Dokl. Akad. Nauk SSSR, n. Ser. 64, 25--28 (1949; Zbl 0032.39201) OpenURL
Hasse, Helmut Proof of a theorem and disproof of a conjecture on the general norm residue symbol. (Beweis eines Satzes und Widerlegung einer Vermutung über das allgemeine Normenrestsymbol.) (German) Zbl 0003.19902 Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. (I, Math.) 1931, 64-69 (1931). Reviewer: F. K. Schmidt (Erlangen) MSC: 11R37 11R20 PDF BibTeX XML Cite \textit{H. Hasse}, Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1931, 64--69 (1931; Zbl 0003.19902) Full Text: EuDML OpenURL
Chevalley, C. Sur la théorie des restes normiques. (French) JFM 56.0166.02 C. R. 191, 426-428 (1930). Reviewer: Pannwitz, Erika, Dr. (Berlin) MSC: 11R37 PDF BibTeX XML Cite \textit{C. Chevalley}, C. R. Acad. Sci., Paris 191, 426--428 (1930; JFM 56.0166.02) Full Text: Gallica OpenURL
Hasse, H. Die Normenresttheorie relativ-Abelscher Zahlkörper als Klassenkörpertheorie im Kleinen. (German) JFM 56.0165.03 J. Reine Angew. Math. 162, 145-154 (1930). MSC: 11R37 PDF BibTeX XML Cite \textit{H. Hasse}, J. Reine Angew. Math. 162, 145--154 (1930; JFM 56.0165.03) Full Text: DOI Crelle EuDML OpenURL
Hasse, H. Neue Begründung und Verallgemeinerung der Theorie des Normenrestsymbols. (German) JFM 56.0165.02 J. Reine Angew. Math. 162, 134-144 (1930). Reviewer: Buchhorn, Lilly, Dr. (Berlin) MSC: 11R37 PDF BibTeX XML Cite \textit{H. Hasse}, J. Reine Angew. Math. 162, 134--144 (1930; JFM 56.0165.02) Full Text: DOI Crelle EuDML OpenURL
Hasse, Helmut Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. I: Klassenkörpertheorie. Ia: Beweise zu Teil I. II: Reziprozitätsgesetz. (German) JFM 56.0165.01 Leipzig: B. G. Teubner I: 134 S. II: iv, 204 S. (1930). Reviewer: Scholz, A., Dr. (Kiel) MSC: 11-02 11R37 PDF BibTeX XML Backlinks: MO OpenURL
Takagi, Teiji Zur Theorie des Kreiskörpers. (German) JFM 53.0146.06 J. Reine Angew. Math. 157, 230-238 (1927). Reviewer: Scholz, A., Dr. (Freiburg i. Br.) MSC: 11R18 11R29 PDF BibTeX XML Cite \textit{T. Takagi}, J. Reine Angew. Math. 157, 230--238 (1927; JFM 53.0146.06) Full Text: DOI Crelle EuDML OpenURL
Hasse, Helmut Direkter Beweis des Zerlegungs- und Vertauschungssatzes für das Hilbertsche Normenrestsymbol in einem algebraischen Zahlkörper im Falle eines Primteilers \({\mathfrak l}\) des Relativgrades \(l\). (German) JFM 50.0106.01 J. Reine Angew. Math. 154, 20-35 (1924). Reviewer: Hasse, Prof. (Halle an der Saale) MSC: 11R37 PDF BibTeX XML Cite \textit{H. Hasse}, J. Reine Angew. Math. 154, 20--35 (1924; JFM 50.0106.01) Full Text: EuDML OpenURL
Hasse, Helmut Das allgemeine Reziprozitätsgesetz und seine Ergänzungssätze in beliebigen algebraischen Zahlkörpern für gewisse, nichtprimäre Zahlen. (German) JFM 50.0105.02 J. Reine Angew. Math. 153, 192-207 (1924). Reviewer: Hasse, Prof. (Halle an der Saale) MSC: 11R37 11A15 PDF BibTeX XML Cite \textit{H. Hasse}, J. Reine Angew. Math. 153, 192--207 (1924; JFM 50.0105.02) Full Text: Crelle EuDML OpenURL
Lietzmann, W. On the theory of \(n\)th power residues in algebraic number fields. II. On \(n\)th norm residues. (Zur Theorie der \(n\)-ten Potenzreste in algebraischen Zahlkörpern. II. Über \(n\)-te Normenreste.) (German) JFM 36.0286.01 Math. Ann. 61, 372-391 (1905). Reviewer: Fueter, Prof. (Basel) MSC: 11R37 11R04 11R20 PDF BibTeX XML Cite \textit{W. Lietzmann}, Math. Ann. 61, 372--391 (1905; JFM 36.0286.01) Full Text: DOI EuDML OpenURL