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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI Link
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 × Cite Format Result Cite Review PDF Full Text: DOI Link
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI Link
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
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 × Cite Format Result Cite Review PDF Full Text: DOI Crelle EuDML
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: Link
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 × Cite Format Result Cite Review PDF Full Text: DOI Crelle EuDML
Vostokov, S. V. The second factor in the reciprocity law. (English) Zbl 0612.12009 J. Sov. Math. 37, 953-958 (1987). MSC: 11S20 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
Coleman, Robert F. The dilogarithm and the norm residue symbol. (English) Zbl 0493.12019 Bull. Soc. Math. Fr. 109, 373-402 (1981). Reviewer: Robert F. Coleman MSC: 11S15 11S80 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
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 × Cite Format Result Cite Review PDF Full Text: MNR
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF Full Text: DOI
Sen, Shankar On explicit reciprocity laws. (English) Zbl 0411.12005 J. Reine Angew. Math. 313, 1-26 (1980). MSC: 11S31 11A15 × Cite Format Result Cite Review PDF Full Text: DOI Crelle EuDML Link
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 × Cite Format Result Cite Review PDF Full Text: DOI
Coleman, Robert F. Division values in local fields. (English) Zbl 0429.12010 Invent. Math. 53, 91-116 (1979). MSC: 11S31 14L05 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: EuDML
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 × Cite Format Result Cite Review PDF Full Text: DOI
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Coates, J.; Wiles, A. Explicit reciprocity laws. (English) Zbl 0358.12001 Astérisque 41-42, 7-17 (1977). Reviewer: Gr. Todorova MSC: 11S31 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: DOI Link
Kneser, Martin Zum expliziten Reziprozitätsgesetz von I. R. Šafarevič. (German) Zbl 0045.32204 Math. Nachr. 6, 89-96 (1951). Reviewer: Ernst Witt MSC: 11R37 × Cite Format Result Cite Review PDF Full Text: DOI
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 11R37 × Cite Format Result Cite Review PDF Full Text: MNR
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF Full Text: EuDML
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 × Cite Format Result Cite Review PDF Full Text: Gallica
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 × Cite Format Result Cite Review PDF Full Text: DOI Crelle EuDML
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 × Cite Format Result Cite Review PDF Full Text: DOI Crelle EuDML
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 × Cite Format Result Cite Review PDF Backlinks: MO
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 × Cite Format Result Cite Review PDF Full Text: DOI Crelle EuDML
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 × Cite Format Result Cite Review PDF Full Text: EuDML
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 × Cite Format Result Cite Review PDF Full Text: Crelle EuDML
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 × Cite Format Result Cite Review PDF Full Text: DOI EuDML Link