Sun, Zhihong Eisenstein and cubic, quartic reciprocity laws. (English) Zbl 07295515 J. Nanjing Univ., Math. Biq. 36, No. 2, 185-200 (2019). MSC: 01A05 11A07 11A15 11E25 PDF BibTeX XML Cite \textit{Z. Sun}, J. Nanjing Univ., Math. Biq. 36, No. 2, 185--200 (2019; Zbl 07295515) Full Text: DOI
Granville, Andrew Number theory revealed: a masterclass. (English) Zbl 1454.11002 Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4158-6/hbk; 978-1-4704-5424-1/ebook). xxviii, 587 p. (2019). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11A55 11B30 11B39 11D09 11D25 11N05 11N25 PDF BibTeX XML Cite \textit{A. Granville}, Number theory revealed: a masterclass. Providence, RI: American Mathematical Society (AMS) (2019; Zbl 1454.11002)
Zhao, Zhengjun 3-class groups of cubic cyclic function fields. (English) Zbl 1424.11162 Turk. J. Math. 42, No. 5, 2607-2620 (2018). MSC: 11R58 11R65 PDF BibTeX XML Cite \textit{Z. Zhao}, Turk. J. Math. 42, No. 5, 2607--2620 (2018; Zbl 1424.11162) Full Text: DOI
Huong, Phạm Lan On the Diophantine equation \(x^3 + y^3 + z^3 = q\). (English) Zbl 1447.11048 Int. J. Number Theory 14, No. 8, 2205-2217 (2018). MSC: 11D25 PDF BibTeX XML Cite \textit{P. L. Huong}, Int. J. Number Theory 14, No. 8, 2205--2217 (2018; Zbl 1447.11048) Full Text: DOI
Demchenko, Oleg; Gurevich, Alexander Reciprocity laws through formal groups. (English) Zbl 1336.11004 Proc. Am. Math. Soc. 141, No. 5, 1591-1596 (2013). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11A15 14L05 PDF BibTeX XML Cite \textit{O. Demchenko} and \textit{A. Gurevich}, Proc. Am. Math. Soc. 141, No. 5, 1591--1596 (2013; Zbl 1336.11004) Full Text: DOI
He, Debiao; Chen, Jianhua; Wang, Yu On Diophantine equation \(3a^2x^4 - By^2 = 1\). (English) Zbl 1231.11033 Ann. Mat. Pura Appl. (4) 189, No. 4, 679-687 (2010). MSC: 11D25 PDF BibTeX XML Cite \textit{D. He} et al., Ann. Mat. Pura Appl. (4) 189, No. 4, 679--687 (2010; Zbl 1231.11033) Full Text: DOI
Helou, Charles; Roll, Ron; Washington, Lawrence C. Power residue character of rational primes. (English) Zbl 1018.11003 J. Ramanujan Math. Soc. 16, No. 1, 19-37 (2001). Reviewer: Franz Lemmermeyer (San Marcos) MSC: 11A15 11R18 PDF BibTeX XML Cite \textit{C. Helou} et al., J. Ramanujan Math. Soc. 16, No. 1, 19--37 (2001; Zbl 1018.11003)
Zaharescu, Alexandru A metric symbol for pairs of polynomials over local fields. (English) Zbl 0972.11111 C. R. Math. Acad. Sci., Soc. R. Can. 22, No. 4, 147-150 (2000). Reviewer: Gabriel D.Villa-Salvador (México) MSC: 11S05 11D25 PDF BibTeX XML Cite \textit{A. Zaharescu}, C. R. Math. Acad. Sci., Soc. R. Can. 22, No. 4, 147--150 (2000; Zbl 0972.11111)
Lemmermeyer, Franz Rational quartic reciprocity. II. (English) Zbl 0878.11040 Acta Arith. 80, No. 3, 273-276 (1997). Reviewer: R.Mollin (Calgary) MSC: 11R16 11A15 PDF BibTeX XML Cite \textit{F. Lemmermeyer}, Acta Arith. 80, No. 3, 273--276 (1997; Zbl 0878.11040) Full Text: DOI EuDML arXiv
Louboutin, Stéphane Norme relative de l’unité fondamentale et 2-rang du groupe des classes de certains corps biquadratiques. (Relative norm of the fundamental unit and 2-rank of the ideal class group of some biquadratic fields). (French) Zbl 0703.11050 Acta Arith. 58, No. 3, 273-288 (1991). Reviewer: S.Louboutin MSC: 11R16 11R29 11R27 PDF BibTeX XML Cite \textit{S. Louboutin}, Acta Arith. 58, No. 3, 273--288 (1991; Zbl 0703.11050) Full Text: DOI EuDML
Ireland, Kenneth; Rosen, Michael A classical introduction to modern number theory. 2nd ed. (English) Zbl 0712.11001 Graduate Texts in Mathematics, 84. New York etc.: Springer-Verlag. xiv, 389 p. DM 98.00 (1990). Reviewer: J.-H.Evertse MSC: 11-01 11Axx 11Gxx 11Nxx 11Rxx 11Txx 11Dxx 11G05 11G40 11D41 14H52 PDF BibTeX XML Cite \textit{K. Ireland} and \textit{M. Rosen}, A classical introduction to modern number theory. 2nd ed. New York etc.: Springer-Verlag (1990; Zbl 0712.11001)
Friesen, C.; Spearman, B. K.; Williams, K. S. Another proof of Eisenstein’s law of cubic reciprocity and its supplement. (English) Zbl 0601.10002 Rocky Mt. J. Math. 16, 395-402 (1986). Reviewer: Heima Hayashi (Kumamoto) MSC: 11A15 11R16 PDF BibTeX XML Cite \textit{C. Friesen} et al., Rocky Mt. J. Math. 16, 395--402 (1986; Zbl 0601.10002) Full Text: DOI
Reshetukha, I. V. A product related to the cubic Gauss sum. (English. Russian original) Zbl 0599.10027 Ukr. Math. J. 37, 611-616 (1985); translation from Ukr. Mat. Zh. 37, No. 6, 745-751 (1985). Reviewer: J.H.Loxton MSC: 11L03 11A15 PDF BibTeX XML Cite \textit{I. V. Reshetukha}, Ukr. Math. J. 37, 611--616 (1985; Zbl 0599.10027); translation from Ukr. Mat. Zh. 37, No. 6, 745--751 (1985) Full Text: DOI
Cassels, J. W. S. A note on the diophantine equation \(x^ 3+y^ 3+z^ 3=3\). (English) Zbl 0556.10007 Math. Comput. 44, 265-266 (1985). Reviewer: B.Richter MSC: 11D25 PDF BibTeX XML Cite \textit{J. W. S. Cassels}, Math. Comput. 44, 265--266 (1985; Zbl 0556.10007) Full Text: DOI
Baker, Alan A concise introduction to the theory of numbers. (English) Zbl 0554.10001 Cambridge etc.: Cambridge University Press. XIII, 95 p. hbk: £15.00; $ 29.95; pbk: £4.95; $ 9.95 (1984). Reviewer: Bernd Richter (Berlin) MSC: 11-01 11Axx 11D09 11D25 11D61 11J81 11H55 11R11 11R27 PDF BibTeX XML
Zantema, H. Global restrictions on ramification in number fields. (English) Zbl 0519.12005 Manuscr. Math. 43, 87-106 (1983). Reviewer: Roelof J. Stroeker (Rotterdam) MSC: 11R21 11R34 11S15 11R16 14F22 11R29 11R09 12G05 11A15 PDF BibTeX XML Cite \textit{H. Zantema}, Manuscr. Math. 43, 87--106 (1983; Zbl 0519.12005) Full Text: DOI EuDML
Shiratani, K. Die Diskriminante der Weierstraßschen elliptischen Funktionen und das Reziprozitätsgesetz in besonderen imaginär-quadratischen Zahlkörpern. (German) Zbl 0163.05101 Abh. Math. Semin. Univ. Hamb. 31, 51-61 (1967). Reviewer: Tomio Kubota MSC: 11R11 PDF BibTeX XML Cite \textit{K. Shiratani}, Abh. Math. Semin. Univ. Hamb. 31, 51--61 (1967; Zbl 0163.05101) Full Text: DOI
Shapiro, A. P. Characteristic polynomials of symmetric matrices. (Russian) Zbl 0108.04202 Sib. Mat. Zh. 3, 280-291 (1962). Reviewer: Chr. U. Jensen MSC: 11C20 11R09 11S05 15B33 11E08 PDF BibTeX XML Cite \textit{A. P. Shapiro}, Sib. Mat. Zh. 3, 280--291 (1962; Zbl 0108.04202)
Habicht, Walter Ein elementarer Beweis des kubischen Reziprozitätsgesetzes. (German) Zbl 0104.26501 Math. Ann. 139, 343-365 (1960). Reviewer: L. Rédei (Szeged) MSC: 11A15 11R16 PDF BibTeX XML Cite \textit{W. Habicht}, Math. Ann. 139, 343--365 (1960; Zbl 0104.26501) Full Text: DOI EuDML
Skolem, Th. Ein elementares Verfahren zur Herleitung der quadratischen Reziprozitätsgesetze in algebraischen Zahlkörpern. (German) Zbl 0005.24504 Skr. Norske Vid.-Akad., Oslo 1932, No. 2, 1-57 (1932). Reviewer: W. Weber (Göttingen) MSC: 11R11 11R16 11A15 PDF BibTeX XML
Dintzl, Erw. The second complementary law to the cubic reciprocity law. (Der zweite Ergänzungssatz des kubischen Reciprocitätsgesetzes.) (German) JFM 30.0184.05 Monatsh. f. Math. 10, 303-306 (1899). Reviewer: Fricke, Prof. (Braunschweig) MSC: 11A15 PDF BibTeX XML Cite \textit{Erw. Dintzl}, Monatsh. Math. Phys. 10, 303--306 (1899; JFM 30.0184.05) Full Text: DOI
Gmeiner, J. A. Extensions to bicubic reciprocity law. (Die Ergänzungssätze zum bikubischen Reciprocitätsgesetze.) (German) JFM 23.0189.02 Wien. Ber. C, 1330-1361 (1890). Reviewer: Simon, P., Dr. (Bonn) MSC: 11A15 PDF BibTeX XML Cite \textit{J. A. Gmeiner}, Wien. Ber. 100, 1330--1361 (1890; JFM 23.0189.02)
Goldscheider, F. The reciprocity law for eighth power residues. (Das Reciprocitätsgesetz der achten Potenzreste.) (German) JFM 21.0178.02 Pr. Berlin. Luisenstädt. Realgymn. 29 S. \(4^{\circ}\) (1889). Reviewer: Simon, P., Dr. (Potsdam) MSC: 11A15 11R16 PDF BibTeX XML
Gegenbauer, L. On the cubic reciprocity law. (Ueber das cubische Reciprocitätsgesetz.) (German) JFM 12.0124.01 Wien. Ber. LXXXI, 1-5 (1880). Reviewer: Simon, Dr. (Berlin) MSC: 11A15 11G15 PDF BibTeX XML Cite \textit{L. Gegenbauer}, Wien. Ber. 81, 1--5 (1880; JFM 12.0124.01)
Dantscher, V. Remarks on the analytic proof of the cubic reciprocity law. (Bemerkungen zum analytischen Beweise des cubischen Reciprocitätsgesetzes.) (German) JFM 09.0132.02 Clebsch Ann. XII, 241-254 (1877). Reviewer: Netto, Prof. (Strassburg) MSC: 11A15 11G15 PDF BibTeX XML Cite \textit{V. Dantscher}, Math. Ann. 12, 241--254 (1877; JFM 09.0132.02) Full Text: DOI Link EuDML
Jacobi, C. G. J. A few remarks on cubic residues. (De residuis cubicis commentatio numerosa.) (Latin) ERAM 002.0047cj J. Reine Angew. Math. 2, 66-69 (1827). Reviewer: Franz Lemmermeyer (Jagstzell) (2015) MSC: 11A15 PDF BibTeX XML Cite \textit{C. G. J. Jacobi}, J. Reine Angew. Math. 2, 66--69 (1827; Zbl 002.0047cj) Full Text: DOI EuDML