Kazhdan, David; Polishchuk, Alexander Schmidt rank of quartics over perfect fields. (English) Zbl 1519.14049 Isr. J. Math. 255, No. 2, 851-869 (2023). Reviewer: Edoardo Ballico (Povo) MSC: 14N07 12E05 15A21 13A02 14R20 PDFBibTeX XMLCite \textit{D. Kazhdan} and \textit{A. Polishchuk}, Isr. J. Math. 255, No. 2, 851--869 (2023; Zbl 1519.14049) Full Text: DOI arXiv
Chen, Ruikai; Mesnager, Sihem Trinomial Planar Functions on Cubic and Quartic Extensions of Finite Fields. arXiv:2303.09229 Preprint, arXiv:2303.09229 [math.NT] (2023). MSC: 11R32 12E10 11G20 11R11 11R16 11T06 12E10 51E15 BibTeX Cite \textit{R. Chen} and \textit{S. Mesnager}, ``Trinomial Planar Functions on Cubic and Quartic Extensions of Finite Fields'', Preprint, arXiv:2303.09229 [math.NT] (2023) Full Text: arXiv OA License
Kulkarni, Raghavendra G. A simpler method to get only the true solutions of cubic and quartic equations using Tschirnhaus transformation. (English) Zbl 1506.12002 Ann. Univ. Paedagog. Crac., Stud. Math. 355(21), 51-56 (2022). MSC: 12D10 PDFBibTeX XMLCite \textit{R. G. Kulkarni}, Ann. Univ. Paedagog. Crac., Stud. Math. 355(21), 51--56 (2022; Zbl 1506.12002) Full Text: DOI
Kaur, Sumandeep; Khanduja, Sudesh K. Discriminant and integral basis of sextic fields defined by \(x^6+ax+b\). (English) Zbl 1502.11107 Commun. Algebra 50, No. 10, 4401-4436 (2022). Reviewer: Radoslav M. Dimitrić (New York) MSC: 11R04 11R29 11-01 11R16 12J10 PDFBibTeX XMLCite \textit{S. Kaur} and \textit{S. K. Khanduja}, Commun. Algebra 50, No. 10, 4401--4436 (2022; Zbl 1502.11107) Full Text: DOI arXiv
Prodanov, Emil M. Classification of the real roots of the quartic equation and their Pythagorean tunes. (English) Zbl 1499.12001 Int. J. Appl. Comput. Math. 7, No. 6, Paper No. 218, 14 p. (2021). MSC: 12D10 26C10 11D41 PDFBibTeX XMLCite \textit{E. M. Prodanov}, Int. J. Appl. Comput. Math. 7, No. 6, Paper No. 218, 14 p. (2021; Zbl 1499.12001) Full Text: DOI arXiv
Drungilas, Paulius; Dubickas, Arturas Reducibility of polynomials after a polynomial substitution. (English) Zbl 1449.12001 Publ. Math. Debr. 96, No. 1-2, 185-194 (2020). Reviewer: Piroska Lakatos (Debrecen) MSC: 12D05 11D25 11D61 PDFBibTeX XMLCite \textit{P. Drungilas} and \textit{A. Dubickas}, Publ. Math. Debr. 96, No. 1--2, 185--194 (2020; Zbl 1449.12001) Full Text: DOI
Kulkarni, Raghavendra G. A novel Tschirnhaus method to get only the true solutions of quartic equations. (English) Zbl 1485.12004 Lect. Mat. 39, No. 1, 5-9 (2018). MSC: 12E12 PDFBibTeX XMLCite \textit{R. G. Kulkarni}, Lect. Mat. 39, No. 1, 5--9 (2018; Zbl 1485.12004) Full Text: Link
Anghel, Nicolae Square roots of real \(3 \times 3\) matrices vs. quartic polynomials with real zeros. (English) Zbl 1424.15013 An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 25, No. 3, 45-58 (2017). MSC: 15A16 12D10 26C10 30C15 PDFBibTeX XMLCite \textit{N. Anghel}, An. Științ. Univ. ``Ovidius'' Constanța, Ser. Mat. 25, No. 3, 45--58 (2017; Zbl 1424.15013) Full Text: DOI
Kulkarni, Raghavendra G. Intersect a quartic to extract its roots. (English) Zbl 1414.12003 Ann. Univ. Paedagog. Crac., Stud. Math. 206(16), 73-76 (2017). MSC: 12D10 PDFBibTeX XMLCite \textit{R. G. Kulkarni}, Ann. Univ. Paedagog. Crac., Stud. Math. 206(16), 73--76 (2017; Zbl 1414.12003) Full Text: DOI
Klaška, Jiří; Skula, Ladislav Law of inertia for the factorization of cubic polynomials – the imaginary case. (English) Zbl 1404.11136 Util. Math. 103, 99-109 (2017). MSC: 11T06 11D25 12E05 PDFBibTeX XMLCite \textit{J. Klaška} and \textit{L. Skula}, Util. Math. 103, 99--109 (2017; Zbl 1404.11136)
Astapov, N. S.; Astapov, I. S. Comparative analysis of solutions to 3rd and 4th order algebraic equations. (Russian. English summary) Zbl 1399.12003 Sib. Zh. Chist. Prikl. Mat. 16, No. 1, 14-28 (2016). MSC: 12E12 12Y05 PDFBibTeX XMLCite \textit{N. S. Astapov} and \textit{I. S. Astapov}, Sib. Zh. Chist. Prikl. Mat. 16, No. 1, 14--28 (2016; Zbl 1399.12003)
Kulkarni, Raghavendra G. Applying a Möbius transformation for solving quartic equations. (English) Zbl 1373.12002 Math. Sci. 41, No. 1, 16-20 (2016). MSC: 12E12 PDFBibTeX XMLCite \textit{R. G. Kulkarni}, Math. Sci. 41, No. 1, 16--20 (2016; Zbl 1373.12002)
Ishitsuka, Yasuhiro Linear determinantal representations of smooth plane cubics over finite fields. arXiv:1604.00115 Preprint, arXiv:1604.00115 [math.AG] (2016). MSC: 14H50 11D25 12Y05 14G15 15A33 BibTeX Cite \textit{Y. Ishitsuka}, ``Linear determinantal representations of smooth plane cubics over finite fields'', Preprint, arXiv:1604.00115 [math.AG] (2016) Full Text: arXiv OA License
Awtrey, Chad; Mistry, Nakhila; Soltz, Nicole Centralizers of transitive permutation groups and applications to Galois theory. (English) Zbl 1332.12005 Missouri J. Math. Sci. 27, No. 1, 16-32 (2015). MSC: 12F10 11R32 11S20 20B35 PDFBibTeX XMLCite \textit{C. Awtrey} et al., Missouri J. Math. Sci. 27, No. 1, 16--32 (2015; Zbl 1332.12005) Full Text: Euclid
Kochetkov, Yu. Yu. Geometry of totally real Galois fields of degree 4. (English. Russian original) Zbl 1394.12002 J. Math. Sci., New York 211, No. 3, 319-326 (2015); translation from Fundam. Prikl. Mat. 19, No. 1, 33-44 (2014). MSC: 12F10 11R16 11R32 11R80 PDFBibTeX XMLCite \textit{Yu. Yu. Kochetkov}, J. Math. Sci., New York 211, No. 3, 319--326 (2015; Zbl 1394.12002); translation from Fundam. Prikl. Mat. 19, No. 1, 33--44 (2014) Full Text: DOI arXiv
Hoffmann, Detlev W.; Sobiech, Marco Witt kernels and Brauer kernels for quartic extensions in characteristic two. (English) Zbl 1364.11092 J. Pure Appl. Algebra 219, No. 10, 4619-4634 (2015). Reviewer: Adam Chapman (Upper Galilee) MSC: 11E81 11E04 11E39 12F05 16K20 PDFBibTeX XMLCite \textit{D. W. Hoffmann} and \textit{M. Sobiech}, J. Pure Appl. Algebra 219, No. 10, 4619--4634 (2015; Zbl 1364.11092) Full Text: DOI arXiv
Awtrey, Chad; Barkley, Brett; Guinn, Jeremy; McCraw, Mackenzie Resolvents, masses, and Galois groups of irreducible quartic polynomials. (English) Zbl 1360.11108 Pi Mu Epsilon J. 13, No. 10, 609-618 (2014). MSC: 11R09 12F10 11S05 PDFBibTeX XMLCite \textit{C. Awtrey} et al., Pi Mu Epsilon J. 13, No. 10, 609--618 (2014; Zbl 1360.11108)
Mahmood, Munir; Hammad, Sali; Mahmood, Ibtihal An efficient algorithm for computing the roots of general quadratic, cubic and quartic equations. (English) Zbl 1316.97005 Int. J. Math. Educ. Sci. Technol. 45, No. 7, 1095-1103 (2014). MSC: 97H30 97N50 65H04 12D10 PDFBibTeX XMLCite \textit{M. Mahmood} et al., Int. J. Math. Educ. Sci. Technol. 45, No. 7, 1095--1103 (2014; Zbl 1316.97005) Full Text: DOI
Wu, Zuohui; Liao, Jun; Xu, Xingzhong; Liu, Heguo A solution of the root of the cubic and quartic equation using determinant. (Chinese. English summary) Zbl 1313.12001 J. Hubei Univ., Nat. Sci. 36, No. 4, 381-384, 388 (2014). MSC: 12D10 15A15 PDFBibTeX XMLCite \textit{Z. Wu} et al., J. Hubei Univ., Nat. Sci. 36, No. 4, 381--384, 388 (2014; Zbl 1313.12001) Full Text: DOI
Mukhamedov, Farrukh; Omirov, Bakhrom; Saburov, Mansoor On cubic equations over \(p\)-adic fields. (English) Zbl 1307.11124 Int. J. Number Theory 10, No. 5, 1171-1190 (2014). Reviewer: Manabu Yoshida (Kumamoto) MSC: 11S05 11D25 11D88 12E10 PDFBibTeX XMLCite \textit{F. Mukhamedov} et al., Int. J. Number Theory 10, No. 5, 1171--1190 (2014; Zbl 1307.11124) Full Text: DOI arXiv
Valentini, Robert C. Galois closures of quartic subfields of rational function fields. (English) Zbl 1372.11106 Finite Fields Appl. 26, 100-103 (2014). MSC: 11R58 11R32 12F10 PDFBibTeX XMLCite \textit{R. C. Valentini}, Finite Fields Appl. 26, 100--103 (2014; Zbl 1372.11106) Full Text: DOI
Sharipov, Ruslan A note on solutions of the cuboid factor equations. arXiv:1209.0723 Preprint, arXiv:1209.0723 [math.NT] (2012). MSC: 11D25 11D72 12E05 14G05 BibTeX Cite \textit{R. Sharipov}, ``A note on solutions of the cuboid factor equations'', Preprint, arXiv:1209.0723 [math.NT] (2012) Full Text: arXiv OA License
Ramsden, John; Sharipov, Ruslan On two algebraic parametrizations for rational solutions of the cuboid equations. arXiv:1208.2587 Preprint, arXiv:1208.2587 [math.NT] (2012). MSC: 11D25 11D72 12E05 14G05 BibTeX Cite \textit{J. Ramsden} and \textit{R. Sharipov}, ``On two algebraic parametrizations for rational solutions of the cuboid equations'', Preprint, arXiv:1208.2587 [math.NT] (2012) Full Text: arXiv OA License
Sharipov, Ruslan On two elliptic curves associated with perfect cuboids. arXiv:1208.1227 Preprint, arXiv:1208.1227 [math.NT] (2012). MSC: 11D25 11D72 12E05 14E05 14G05 14H52 BibTeX Cite \textit{R. Sharipov}, ``On two elliptic curves associated with perfect cuboids'', Preprint, arXiv:1208.1227 [math.NT] (2012) Full Text: arXiv OA License
Shmakov, Sergei L. A universal method of solving quartic equations. (English) Zbl 1247.12004 Int. J. Pure Appl. Math. 71, No. 2, 251-259 (2011). Reviewer: Mowaffaq Hajja (Irbid) MSC: 12E12 12-08 65H04 PDFBibTeX XMLCite \textit{S. L. Shmakov}, Int. J. Pure Appl. Math. 71, No. 2, 251--259 (2011; Zbl 1247.12004) Full Text: Link
Kochetkov, Yu. Yu. On the geometry of Galois cubic fields. (English. Russian original) Zbl 1273.11154 Math. Notes 89, No. 1, 150-155 (2011); translation from Mat. Zametki 89, No. 1, 139-144 (2011). Reviewer: Mowaffaq Hajja (Irbid) MSC: 11R16 12F10 PDFBibTeX XMLCite \textit{Yu. Yu. Kochetkov}, Math. Notes 89, No. 1, 150--155 (2011; Zbl 1273.11154); translation from Mat. Zametki 89, No. 1, 139--144 (2011) Full Text: DOI
Haramaty, Elad; Shpilka, Amir On the structure of cubic and quartic polynomials. (English) Zbl 1293.11104 Proceedings of the 42nd annual ACM symposium on theory of computing, STOC ’10. Cambridge, MA, USA, June 5–8, 2010. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-60558-817-9). 331-340 (2010). MSC: 11T06 12Y05 PDFBibTeX XMLCite \textit{E. Haramaty} and \textit{A. Shpilka}, in: Proceedings of the 42nd annual ACM symposium on theory of computing, STOC '10. Cambridge, MA, USA, June 5--8, 2010. New York, NY: Association for Computing Machinery (ACM). 331--340 (2010; Zbl 1293.11104) Full Text: DOI arXiv
Hoshi, Akinari On the simplest quartic fields and related Thue equations. (English) Zbl 1243.12002 Suzuki, Masakazu (ed.) et al., The joint conference of ASCM 2009 and MACIS 2009. 9th international conference on Asian symposium on computer mathematics and 3rd international conference on mathematical aspects of computer and information sciences, Fukuoka, Japan, December 14–17, 2009. Selected papers. Fukuoka: Kyushu University, Faculty of Mathematics. COE Lecture Note 22, 320-329 (2009). Reviewer: Günter Lettl (Graz) MSC: 12E10 11D25 PDFBibTeX XMLCite \textit{A. Hoshi}, COE Lect. Note 22, 320--329 (2009; Zbl 1243.12002) Full Text: arXiv
Hoshi, Akinari; Miyake, Katsuya On the field intersection problem of quartic generic polynomials via formal Tschirnhausen transformation. (English) Zbl 1236.11090 Comment. Math. Univ. St. Pauli 58, No. 1, 51-89 (2009). Reviewer: Bernat Plans (Barcelona) MSC: 11R16 11R20 12E25 12F10 12F12 PDFBibTeX XMLCite \textit{A. Hoshi} and \textit{K. Miyake}, Comment. Math. Univ. St. Pauli 58, No. 1, 51--89 (2009; Zbl 1236.11090) Full Text: arXiv
Komatsu, Toru Generalized Kummer theory and its applications. (English) Zbl 1188.11054 Ann. Math. Blaise Pascal 16, No. 1, 127-138 (2009). Reviewer: Bouchaïb Sodaïgui (Valenciennes) MSC: 11R20 12E10 11R16 PDFBibTeX XMLCite \textit{T. Komatsu}, Ann. Math. Blaise Pascal 16, No. 1, 127--138 (2009; Zbl 1188.11054) Full Text: DOI Numdam EuDML
Auckly, Dave Solving the quartic with a pencil. (English) Zbl 1134.12001 Am. Math. Mon. 114, No. 1, 29-39 (2007). Reviewer: Juan Gerardo Alcazar (Alcala da Henares) MSC: 12E12 14Q05 14C21 PDFBibTeX XMLCite \textit{D. Auckly}, Am. Math. Mon. 114, No. 1, 29--39 (2007; Zbl 1134.12001) Full Text: DOI arXiv
Schönhage, Arnold Polynomial root separation examples. (English) Zbl 1158.12300 J. Symb. Comput. 41, No. 10, 1080-1090 (2006). MSC: 12D10 68W30 PDFBibTeX XMLCite \textit{A. Schönhage}, J. Symb. Comput. 41, No. 10, 1080--1090 (2006; Zbl 1158.12300) Full Text: DOI
Brunotte, Horst On cubic CNS polynomials with three real roots. (English) Zbl 1064.11005 Acta Sci. Math. 70, No. 3-4, 495-504 (2004). Reviewer: Joachim Piehler (Merseburg) MSC: 11C08 11R04 11R16 11A63 12D99 PDFBibTeX XMLCite \textit{H. Brunotte}, Acta Sci. Math. 70, No. 3--4, 495--504 (2004; Zbl 1064.11005)
Williams, Kenneth S. On real cubic fields with a unique fundamental unit. (English) Zbl 1047.11104 Far East J. Math. Sci. (FJMS) 12, No. 1, 1-7 (2004). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R16 11R27 12D10 PDFBibTeX XMLCite \textit{K. S. Williams}, Far East J. Math. Sci. (FJMS) 12, No. 1, 1--7 (2004; Zbl 1047.11104)
Holing, Kent When does the quartic equation have constructible roots? Additional comment on the Galois group. (Norwegian. English summary) Zbl 1061.11053 Normat 51, No. 2, 80-82 (2003). MSC: 11R09 11R32 12E10 12F10 PDFBibTeX XMLCite \textit{K. Holing}, Normat 51, No. 2, 80--82 (2003; Zbl 1061.11053)
Brunotte, Horst Characterization of CNS trinomials. (English) Zbl 1026.11077 Acta Sci. Math. 68, No. 3-4, 673-679 (2002). Reviewer: Lajos Hajdu (Debrecen) MSC: 11R04 11R16 11R21 12D99 PDFBibTeX XMLCite \textit{H. Brunotte}, Acta Sci. Math. 68, No. 3--4, 673--679 (2002; Zbl 1026.11077)
Albu, Toma Some examples in cogalois theory with applications to elementary field arithmetic. (English) Zbl 1044.12002 J. Algebra Appl. 1, No. 1, 1-29 (2002). Reviewer: Gabriel D. Villa-Salvador (México D.F.) MSC: 12F05 12F10 12E30 12E10 11R32 PDFBibTeX XMLCite \textit{T. Albu}, J. Algebra Appl. 1, No. 1, 1--29 (2002; Zbl 1044.12002) Full Text: DOI
Takahashi, Takeshi Galois points on normal quartic surfaces. (English) Zbl 1036.14022 Osaka J. Math. 39, No. 3, 647-663 (2002). Reviewer: Jannis A. Antoniadis (Iraklion) MSC: 14J70 12F10 14J28 14H05 14J17 PDFBibTeX XMLCite \textit{T. Takahashi}, Osaka J. Math. 39, No. 3, 647--663 (2002; Zbl 1036.14022)
Beslin, Scott J.; Baney, Douglas J. Another look at factoring polynomials. (English) Zbl 1001.12001 Coll. Math. J. 32, No. 4, 273-275 (2001). Reviewer: George M.Rassias (Athens) MSC: 12D05 12D10 PDFBibTeX XMLCite \textit{S. J. Beslin} and \textit{D. J. Baney}, Coll. Math. J. 32, No. 4, 273--275 (2001; Zbl 1001.12001) Full Text: DOI
Edwards, B. Carter; Shurman, Jerry Folding quartic roots. (English) Zbl 0995.12002 Math. Mag. 74, No. 1, 19-25 (2001). Reviewer: John N.Mordeson (Omaha) MSC: 12E12 12D05 PDFBibTeX XMLCite \textit{B. C. Edwards} and \textit{J. Shurman}, Math. Mag. 74, No. 1, 19--25 (2001; Zbl 0995.12002) Full Text: DOI
Swan, Richard G. Hilbert’s theorem on positive ternary quartics. (English) Zbl 1026.11045 Bayer-Fluckiger, Eva (ed.) et al., Quadratic forms and their applications. Proceedings of the conference, University College Dublin, Ireland, July 5-9, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 272, 287-292 (2000). Reviewer: N.Schwartz (Passau) MSC: 11E10 13J30 11E76 12D15 PDFBibTeX XMLCite \textit{R. G. Swan}, Contemp. Math. 272, 287--292 (2000; Zbl 1026.11045)
Miura, Kei Field theory for function fields of singular plane quartic curves. (English) Zbl 0986.14016 Bull. Aust. Math. Soc. 62, No. 2, 193-204 (2000). Reviewer: Augusto Nobile (Baton Rouge) MSC: 14H05 14H20 12F20 PDFBibTeX XMLCite \textit{K. Miura}, Bull. Aust. Math. Soc. 62, No. 2, 193--204 (2000; Zbl 0986.14016) Full Text: DOI
Cremona, J. E. Reduction of binary cubic and quartic forms. (English) Zbl 0927.11020 LMS J. Comput. Math. 2, 62-92 (1999). Reviewer: A.Pethő (Debrecen) MSC: 11E76 12Y05 11R16 11R29 11H55 PDFBibTeX XMLCite \textit{J. E. Cremona}, LMS J. Comput. Math. 2, 64--94 (1999; Zbl 0927.11020) Full Text: DOI Link
Nassirou, Lo Study of the level of certain fields. (Étude du niveau de certains corps.) (French) Zbl 0920.11023 Bull. Belg. Math. Soc. - Simon Stevin 6, No. 1, 131-146 (1999). Reviewer: K.Szymiczek (Tychy) MSC: 11E25 12D15 PDFBibTeX XMLCite \textit{L. Nassirou}, Bull. Belg. Math. Soc. - Simon Stevin 6, No. 1, 131--146 (1999; Zbl 0920.11023)
Holing, Kent Ladder problems revisited. (Norwegian. English summary) Zbl 0914.00005 Normat 45, No. 2, 62-78 (1997). MSC: 00A08 12E12 PDFBibTeX XMLCite \textit{K. Holing}, Normat 45, No. 2, 62--78 (1997; Zbl 0914.00005)
Faucette, William M. A geometric interpretation of the solution of the general quartic polynomial. (English) Zbl 0864.12001 Am. Math. Mon. 103, No. 1, 51-57 (1996). Reviewer: T.Soundararajan (Madurai) MSC: 12E10 12F10 PDFBibTeX XMLCite \textit{W. M. Faucette}, Am. Math. Mon. 103, No. 1, 51--57 (1996; Zbl 0864.12001) Full Text: DOI
Ennola, V. Cubic number fields with exceptional units. (English) Zbl 0732.11054 Computational number theory, Proc. Colloq., Debrecen/Hung. 1989, 103-128 (1991). Reviewer: H.J.Godwin (Egham) MSC: 11R16 11R27 11R29 11Y40 12F05 PDFBibTeX XML
Isbell, John A freshman calculus proof that real quartics factor. (English) Zbl 0743.12003 Am. Math. Mon. 98, No. 8, 749-751 (1991). Reviewer: W.Narkiewicz (Wrocław) MSC: 12D05 PDFBibTeX XMLCite \textit{J. Isbell}, Am. Math. Mon. 98, No. 8, 749--751 (1991; Zbl 0743.12003) Full Text: DOI
Treur, Jan Polynomial extensions of skew fields. (English) Zbl 0729.16009 J. Pure Appl. Algebra 67, No. 1, 73-93 (1990). Reviewer: L.G.Makar-Limanov (Detroit) MSC: 16K20 12E15 16S20 PDFBibTeX XMLCite \textit{J. Treur}, J. Pure Appl. Algebra 67, No. 1, 73--93 (1990; Zbl 0729.16009) Full Text: DOI
Li, Delang Defining equations and trace forms of cubic cyclic fields. (English) Zbl 0676.12001 Sci. China, Ser. A 32, No. 1, 52-61 (1989). Reviewer: N.Vila MSC: 11R16 12E12 11E12 PDFBibTeX XMLCite \textit{D. Li}, Sci. China, Ser. A 32, No. 1, 52--61 (1989; Zbl 0676.12001)
Nakamula, Ken A table for pure cubic fields. (English) Zbl 0663.12005 Investigations in number theory, Adv. Stud. Pure Math. 13, 461-477 (1988). Reviewer: G.Gras MSC: 11R16 12-04 65A05 11R23 PDFBibTeX XML
Halbritter, Ulrich Berechnung der Werte von Zetafunktionen totalreeller kubischer Zahlkörper an ganzzahligen Stellen mittels verallgemeinerter Dedekindscher Summen. II. (Computation of values of zeta-functions of totally real cubic number fields at integers by means of generalized Dedekind sums. II.). (German) Zbl 0658.12004 Result. Math. 13, No. 1-2, 99-134 (1988). Reviewer: M.Pohst MSC: 11R42 11R16 11R80 12-04 PDFBibTeX XMLCite \textit{U. Halbritter}, Result. Math. 13, No. 1--2, 99--134 (1988; Zbl 0658.12004) Full Text: DOI
Dueck, G.; Williams, H. C. Corrigendum to: “Computation of the class number and class group of a complex cubic field”. (English) Zbl 0652.12003 Math. Comput. 50, No. 182, 223-231 (1988). Reviewer: K.Lakkis MSC: 11R16 11R23 12-04 68Q25 12D99 PDFBibTeX XMLCite \textit{G. Dueck} and \textit{H. C. Williams}, Math. Comput. 50, No. 182, 223--231 (1988; Zbl 0652.12003)
Llorente, Pascual; Quer, Jordi On totally real cubic fields with discriminant \(D<10^ 7\). (English) Zbl 0651.12001 Math. Comput. 50, No. 182, 581-594 (1988). Reviewer: K.Peeva MSC: 12-04 11R16 11R80 PDFBibTeX XMLCite \textit{P. Llorente} and \textit{J. Quer}, Math. Comput. 50, No. 182, 581--594 (1988; Zbl 0651.12001) Full Text: DOI
Hardy, Kenneth; Hudson, R. H.; Richman, D.; Williams, Kenneth S.; Holtz, N. M. Calculation of the class numbers of imaginary cyclic quartic fields. (English) Zbl 0624.12004 Math. Comput. 49, 615-620 (1987). MSC: 11R21 11R23 12-04 PDFBibTeX XMLCite \textit{K. Hardy} et al., Math. Comput. 49, 615--620 (1987; Zbl 0624.12004) Full Text: DOI
Williams, Kenneth S. The class number two problem for certain quartic fields. (English) Zbl 0615.12011 Numerical mathematics and computing, Proc. 16th Conf., Winnipeg/Manit. 1986, Congr. Numerantium 56, 63-70 (1987). Reviewer: R.Mollin MSC: 11R23 11R16 12-04 PDFBibTeX XML
Buchmann, Johannes On the computation of units and class numbers by a generalization of Lagrange’s algorithm. (English) Zbl 0615.12001 J. Number Theory 26, 8-30 (1987). Reviewer: C.Levesque MSC: 12-04 11J70 11R23 11R27 11R52 11R16 PDFBibTeX XMLCite \textit{J. Buchmann}, J. Number Theory 26, 8--30 (1987; Zbl 0615.12001) Full Text: DOI
Azuhata, Takashi On the calculation of a system of fundamental units of an algebraic number field. (English) Zbl 0637.12003 Class numbers and fundamental units of algebraic number fields, Proc. Int. Conf., Katata/Jap. 1986, 17-31 (1986). Reviewer: J.Buchmann MSC: 11R27 12-04 11R16 PDFBibTeX XML
Scarowsky, Manny; Boyarsky, Abraham On the computation of the class numbers of some cubic fields. (English) Zbl 0626.12005 Int. J. Math. Math. Sci. 9, 797-800 (1986). Reviewer: R.J.Stroeker MSC: 11R16 11R23 11D25 12-04 PDFBibTeX XMLCite \textit{M. Scarowsky} and \textit{A. Boyarsky}, Int. J. Math. Math. Sci. 9, 797--800 (1986; Zbl 0626.12005) Full Text: DOI EuDML
Williams, Kenneth S. Calculation of the class numbers of certain quartic fields. (English) Zbl 0615.12008 Class numbers and fundamental units of algebraic number fields, Proc. Int. Conf., Katata/Jap. 1986, 139-150 (1986). MSC: 11R23 12-04 11R16 PDFBibTeX XML
Hong, Kyunghwa The solution in quaternions of Fermat type equation. (English) Zbl 0609.10009 Math. Rep., Toyama Univ. 9, 33-41 (1986). Reviewer: M.E.Keating MSC: 11D25 12E15 PDFBibTeX XMLCite \textit{K. Hong}, Math. Rep., Toyama Univ. 9, 33--41 (1986; Zbl 0609.10009)
Tennenhouse, M.; Williams, H. C. A note on class-number one in certain real quadratic and pure cubic fields. (English) Zbl 0589.12003 Math. Comput. 46, 333-336 (1986). Reviewer: V.Ennola MSC: 12-04 11R11 11R16 11R23 PDFBibTeX XMLCite \textit{M. Tennenhouse} and \textit{H. C. Williams}, Math. Comput. 46, 333--336 (1986; Zbl 0589.12003) Full Text: DOI
Cohn, Harvey; Deutsch, Jesse Use of a computer scan to prove \({\mathbb{Q}}(\sqrt{2+\sqrt{2}})\) and \({\mathbb{Q}}(\sqrt{3+\sqrt{2}})\) are Euclidean. (English) Zbl 0585.12002 Math. Comput. 46, 295-299 (1986). Reviewer: H.J.Godwin MSC: 11R16 12-04 PDFBibTeX XMLCite \textit{H. Cohn} and \textit{J. Deutsch}, Math. Comput. 46, 295--299 (1986; Zbl 0585.12002) Full Text: DOI
Åman, J. E.; d’Inverno, R. A.; Joly, G. C.; MacCallum, M. A. H. Quartic equations and algorithms for Riemann tensor classification. (English) Zbl 0583.68013 EUROSAM 84, Symbolic and algebraic computation, Proc. int. Symp., Cambridge/Engl. 1984, Lect. Notes Comput. Sci. 174, 47-58 (1984). MSC: 68W30 65H05 83C05 12D10 53A45 PDFBibTeX XML
Dussaud, René On a Kummerian distribution of roots of unity. (Sur une répartition kummérienne des racines de l’unité.) (French) Zbl 0576.12023 Publ. Cent. Rech. Math. Pures, Sér. I 18(1983/84), 1-5 (1984). Reviewer: Paulo Ribenboim (Kingston/Ontario) MSC: 12E12 11R18 11D41 11R32 12F10 11R16 PDFBibTeX XMLCite \textit{R. Dussaud}, Publ. Cent. Rech. Math. Pures, Sér. I 18, 1--5 (1984; Zbl 0576.12023)
Heider, Franz-Peter; Kolvenbach, Paulgerd The construction of SL(2,3)-polynomials. (English) Zbl 0566.12003 J. Number Theory 19, 392-411 (1984). Reviewer: N.Vila MSC: 11R32 20F29 11R80 12E12 12F10 PDFBibTeX XMLCite \textit{F.-P. Heider} and \textit{P. Kolvenbach}, J. Number Theory 19, 392--411 (1984; Zbl 0566.12003) Full Text: DOI
Adams, William W. Splitting of quartic polynomials. (English) Zbl 0551.12017 Math. Comput. 43, 329-343 (1984). Reviewer: H.Cohn MSC: 12D05 11B37 12F10 11T06 12-04 PDFBibTeX XMLCite \textit{W. W. Adams}, Math. Comput. 43, 329--343 (1984; Zbl 0551.12017) Full Text: DOI
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 PDFBibTeX XMLCite \textit{H. Zantema}, Manuscr. Math. 43, 87--106 (1983; Zbl 0519.12005) Full Text: DOI EuDML
Ozeki, K. A certain property of polynomials. (English) Zbl 0541.12011 Aequationes Math. 25, 247-252 (1982). Reviewer: K.Chandrasekhara Rao MSC: 12E05 12E12 11R16 11R27 PDFBibTeX XMLCite \textit{K. Ozeki}, Aequationes Math. 25, 247--252 (1982; Zbl 0541.12011) Full Text: DOI EuDML
Uchiyama, Saburô; Yorinaga, Masataka On the difference \(f^3(x)-g^2(x)\). (English) Zbl 0526.12013 Tsukuba J. Math. 6, 215-230 (1982). Reviewer: Harvey Cohn MSC: 12D99 11C08 12-04 11D25 PDFBibTeX XMLCite \textit{S. Uchiyama} and \textit{M. Yorinaga}, Tsukuba J. Math. 6, 215--230 (1982; Zbl 0526.12013) Full Text: DOI
Llorente, P.; Oneto, A. V. On the real cubic fields. (English) Zbl 0511.12005 Math. Comput. 39, 689-692 (1982). MSC: 11R16 11R80 11R23 12-04 11R09 PDFBibTeX XMLCite \textit{P. Llorente} and \textit{A. V. Oneto}, Math. Comput. 39, 689--692 (1982; Zbl 0511.12005) Full Text: DOI
Stark, H. M. Values of zeta and L-functions. (English) Zbl 0509.12012 Abh. Braunschw. Wiss. Ges. 33, 71-83 (1982). MSC: 11R42 11F03 11R16 11R23 12H05 11M06 PDFBibTeX XMLCite \textit{H. M. Stark}, Abh. Braunschw. Wiss. Ges. 33, 71--83 (1982; Zbl 0509.12012)
Schinzel, Andrzej Families of curves having each an integer point. (English) Zbl 0494.10007 Acta Arith. 40, 399-420 (1982). MSC: 11D99 11D41 12E05 11D04 11D25 PDFBibTeX XMLCite \textit{A. Schinzel}, Acta Arith. 40, 399--420 (1982; Zbl 0494.10007) Full Text: DOI EuDML
Parry, Charles J. On the class number of relative quadratic fields. (English) Zbl 0401.12008 Math. Comput. 32, 1261-1270 (1978). MSC: 11R23 12-04 11R80 11R16 PDFBibTeX XMLCite \textit{C. J. Parry}, Math. Comput. 32, 1261--1270 (1978; Zbl 0401.12008) Full Text: DOI
Shanks, Daniel Errata to: Über die Lösung einiger unbestimmten Gleichungen vierten Grades. (German) Zbl 0385.12002 Math. Comput. 31, 1049-1050 (1977). MSC: 11R16 12-04 11R27 11R42 PDFBibTeX XMLCite \textit{D. Shanks}, Math. Comput. 31, 1049--1050 (1977; Zbl 0385.12002) Full Text: DOI
Halter-Koch, Franz Eine Bemerkung über kubische Einheiten. (German) Zbl 0352.12005 Arch. Math. 27, 593-595 (1976). MSC: 11R16 11R27 12D99 PDFBibTeX XMLCite \textit{F. Halter-Koch}, Arch. Math. 27, 593--595 (1976; Zbl 0352.12005) Full Text: DOI
Barrucand, Pierre; Williams, H. C.; Baniuk, L. A computational technique for determining the class number of a pure cubic field. (English) Zbl 0324.12005 Math. Comput. 30, 312-323 (1976). MSC: 11R23 11R16 12-04 11R42 PDFBibTeX XMLCite \textit{P. Barrucand} et al., Math. Comput. 30, 312--323 (1976; Zbl 0324.12005) Full Text: DOI
Coray, D. F. Algebraic points on cubic hypersurfaces. (English) Zbl 0294.14012 Acta Arith. 30, 267-296 (1976). MSC: 14G05 11D25 12F05 11D88 14J20 PDFBibTeX XMLCite \textit{D. F. Coray}, Acta Arith. 30, 267--296 (1976; Zbl 0294.14012) Full Text: DOI EuDML
Coray, Daniel Sur les points algébriques des hypersurfaces de degré 3. (French) Zbl 0294.14011 C. R. Acad. Sci., Paris, Sér. A 280, 181-182 (1975). MSC: 14G05 12F05 14J20 11D25 11D88 PDFBibTeX XMLCite \textit{D. Coray}, C. R. Acad. Sci., Paris, Sér. A 280, 181--182 (1975; Zbl 0294.14011)
Birch, B. J.; Chowla, Sarvadaman; Hall, M. jun.; Schinzel, Andrzej On the difference \(x^ 3 -y^ 2\). (English) Zbl 0144.03901 Norske Vid. Selsk. Forhdl. 38, 65-69 (1965). Reviewer: S. Christofferson MSC: 12D99 11C08 11D25 PDFBibTeX XMLCite \textit{B. J. Birch} et al., Norske Vid. Selsk. Forhdl. 38, 65--69 (1965; Zbl 0144.03901)
Lester, Caroline A. A determination of the automorphisms of certain algebraic fields. (English) Zbl 0019.04902 Duke Math. J. 4, 277-290 (1938). Reviewer: Olga Taussky (London) MSC: 12F10 PDFBibTeX XMLCite \textit{C. A. Lester}, Duke Math. J. 4, 277--290 (1938; Zbl 0019.04902) Full Text: DOI
Leire, P. A solution of the equation \(x^4+ax^2+bx+c=0\). (En Oplösning af Ligningen \[ x^4+ax^2+bx+c=0 \] .) (Danish) JFM 09.0063.03 Zeuthen Tidsskr. (4) I, 117-118 (1877). Reviewer: Gram, Dr. (Kopenhagen) MSC: 12E12 PDFBibTeX XMLCite \textit{P. Leire}, Zeuthen Tidsskr. (4) 1, 117--118 (1877; JFM 09.0063.03)
Lampe, E. Geometric tasks about the cubic equations together with an appendix with taks about biquadratic equations. (Geometrische Aufgaben zu den cubischen Gleichungen nebst einem Anhange mit Aufgaben über biquadritische Gleichungen.) (German) JFM 09.0063.02 Berlin. H. W. Müller (1877). Reviewer: Ohrtmann, Dr. (Berlin) MSC: 12E12 12F99 12-01 PDFBibTeX XML
Valeriani, V. Analytic solution of complete biquadratic equations. (Soluzione analitica delle equazioni biquadratische complete.) (Italian) JFM 07.0048.01 Battaglini G. XIII, 99-107 (1875). Reviewer: Netto, Dr. (Berlin) MSC: 12D10 12E10 PDFBibTeX XMLCite \textit{V. Valeriani}, Battaglini G. 13, 99--107 (1875; JFM 07.0048.01)
Casey, J. On the equation of the squares of the differences of the roots of a biquadratic. (English) JFM 07.0047.02 Trans. of Dublin. 1875 (1875). Reviewer: Casey, Prof. (Dublin) (Ohrtmann, Dr. (Berlin)) MSC: 12D10 12E10 PDFBibTeX XML
Hill, G. On the solution of cubic and biquadratic equations. (English) JFM 07.0047.01 Analyst II, 4-8 (1875). Reviewer: Glaisher, Prof. (Cambridge) (Ohrtmann, Dr. (Berlin)) MSC: 12D10 12E10 PDFBibTeX XMLCite \textit{G. Hill}, Analyst 2, 4--8 (1875; JFM 07.0047.01) Full Text: DOI
Azzarelli, M. Solution of equations of degree \(3\) and \(4\) by means of the linear substitution \(z=\frac{my+n}{y+1}\). (Risoluzione delle equazione di \(3^{0}\) e \(4^{0}\) grado per mezzo della sostituzione lineare \(z=\frac{my + n}{y + 1}.\).) (Italian) JFM 03.0030.01 Att. d. Acc. d. N. Linc. XXIV, 83-90 (1871). Reviewer: Jung, Prof. (Mailand) (Ohrtmann, Dr. (Berlin)) MSC: 11D25 12D99 PDFBibTeX XMLCite \textit{M. Azzarelli}, Rom. Acc. P. d. N. L. 24, 83--90 (1871; JFM 03.0030.01)
Cayley, A. Note on the Discriminant of a binary Quartic. (English) JFM 02.0075.01 Quart. J. X, 23 (1869). Reviewer: Henrici, Prof. (London) MSC: 14H50 15A63 12D10 PDFBibTeX XMLCite \textit{A. Cayley}, Quart. J. 10, 23 (1869; JFM 02.0075.01)
Cayley, A. Note. (original title). (Note.) (English) JFM 02.0056.01 Quart. J. X, 56-57 (1869). Reviewer: Henrici, Prof. (London) MSC: 12E12 PDFBibTeX XMLCite \textit{A. Cayley}, Quart. J. 10, 56--57 (1869; JFM 02.0056.01)
Walker, J. J. On the anharmonic ratio sextic. (original title). (On the anharmonic-ratio sextic.) (English) JFM 02.0055.03 Quart. J. X, 53-56 (1869). Reviewer: Henrici, Prof. (London) MSC: 12E12 PDFBibTeX XMLCite \textit{J. J. Walker}, Quart. J. 10, 53--56 (1869; JFM 02.0055.03)
Tortolini, B. Resolution of a problem concerning the equations of third and fourth degree. (Soluzione di un problema relativo alle equazioni di \(3^\circ\) e \(4^\circ\) grado.) (Italian) JFM 02.0052.04 Atti d. Acc. P. dei N. Lincei XXII, 166-168 (1869). Reviewer: Jung, G., Dr. (Mailand) (transl. by Ohrtmann, Dr. (Berlin)). MSC: 12E12 PDFBibTeX XMLCite \textit{B. Tortolini}, Rom. Acc. P. d. N. L. 22, 166--168 (1869; JFM 02.0052.04)