Costa Marques, Fernando; Pombo, Dinamérico P. jun. Rational solutions of certain Diophantine equations. 2nd edition. (Soluções racionais de certas equações Diofantinas.) (Portuguese) Zbl 07765425 Textos de Matemática (Rio de Janeiro). Rio de Janeiro: Editora Instituto de Matemática, Universidade Federal do Rio de Janeiro (ISBN 978-65-86502-02-2). 37 p. (2023). Reviewer: Florian Luca (Johannesburg) MSC: 11D25 11D41 11-01 11D88 PDFBibTeX XMLCite \textit{F. Costa Marques} and \textit{D. P. Pombo jun.}, Soluções racionais de certas equações Diofantinas (Portuguese). 2nd edition. Rio de Janeiro: Editora Instituto de Matemática, Universidade Federal do Rio de Janeiro (2023; Zbl 07765425)
Lozano-Robledo, Álvaro Number theory and geometry. An introduction to arithmetic geometry. (English) Zbl 1432.11002 Pure and Applied Undergraduate Texts 35. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-5016-8/hbk; 978-1-4704-5190-5/ebook). xv, 488 p. (2019). Reviewer: Luis Gallardo (Brest) MSC: 11-01 11Axx 11D09 11D25 11G05 97F60 PDFBibTeX XMLCite \textit{Á. Lozano-Robledo}, Number theory and geometry. An introduction to arithmetic geometry. Providence, RI: American Mathematical Society (AMS) (2019; Zbl 1432.11002)
Hambleton, Samuel A.; Williams, Hugh C. Cubic fields with geometry. (English) Zbl 1451.11001 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Cham: Springer (ISBN 978-3-030-01402-5/hbk; 978-3-030-01404-9/ebook). xix, 493 p. (2018). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11-02 11D25 11D59 11H50 11Y40 11Y65 14Q10 11R16 PDFBibTeX XMLCite \textit{S. A. Hambleton} and \textit{H. C. Williams}, Cubic fields with geometry. Cham: Springer (2018; Zbl 1451.11001) Full Text: DOI
Ash, Avner; Gross, Robert Elliptic tales. Curves, counting, and number theory. Reprint of the 2012 hardback edition. (English) Zbl 1300.11054 Princeton, NJ: Princeton University Press (ISBN 978-0-691-16350-5/pbk; 978-1-400-84171-4/ebook). xvii, 253 p. (2015). MSC: 11-01 11G05 11D25 14H52 14G10 PDFBibTeX XMLCite \textit{A. Ash} and \textit{R. Gross}, Elliptic tales. Curves, counting, and number theory. Reprint of the 2012 hardback edition. Princeton, NJ: Princeton University Press (2015; Zbl 1300.11054) Full Text: DOI
Rashed, Roshdi; Houzel, Christian The “Arithmetica” of Diophantus. A historical and mathematical reading. (Les “Arithmétiques” de Diophante. Lecture historique et mathématique.) (French) Zbl 1302.01002 Scientia Graeco-Arabica 11. Berlin: De Gruyter (ISBN 978-3-11-033593-4/hbk; 978-3-11-033648-1/ebook). x, 629 p. (2013). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 01-02 01A20 11-03 11D09 11D25 11G05 PDFBibTeX XMLCite \textit{R. Rashed} and \textit{C. Houzel}, Les ``Arithmétiques'' de Diophante. Lecture historique et mathématique. Berlin: De Gruyter (2013; Zbl 1302.01002) Full Text: DOI
Tzanakis, Nikos Elliptic Diophantine equations. A concrete approach via the elliptic logarithm. (English) Zbl 1311.11023 De Gruyter Series in Discrete Mathematics and Applications 2. Berlin: de Gruyter (ISBN 978-3-11-028091-3/hbk; 978-3-11-028114-9/ebook). xvi, 179 p. (2013). Reviewer: Maciej Ulas (Kraków) MSC: 11D25 11D41 11-02 11G05 11Y50 PDFBibTeX XMLCite \textit{N. Tzanakis}, Elliptic Diophantine equations. A concrete approach via the elliptic logarithm. Berlin: de Gruyter (2013; Zbl 1311.11023)
Cho, Yeol Je; Rassias, Themistocles M.; Saadati, Reza Stability of functional equations in random normed spaces. (English) Zbl 1281.46001 Springer Optimization and Its Applications 86. New York, NY: Springer (ISBN 978-1-4614-8476-9/hbk; 978-1-4614-8477-6/ebook). xix, 246 p. (2013). Reviewer: Mohammad Sal Moslehian (Mashhad) MSC: 46-02 39-02 39B52 46S10 46S40 PDFBibTeX XMLCite \textit{Y. J. Cho} et al., Stability of functional equations in random normed spaces. New York, NY: Springer (2013; Zbl 1281.46001) Full Text: DOI
Aigner, Martin Markov’s theorem and 100 years of the uniqueness conjecture. A mathematical journey from irrational numbers to perfect matchings. (English) Zbl 1276.00006 Cham: Springer (ISBN 978-3-319-00887-5/hbk; 978-3-319-00888-2/ebook). x, 257 p. (2013). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 00A05 11-01 11J06 11D25 05-01 20-01 PDFBibTeX XMLCite \textit{M. Aigner}, Markov's theorem and 100 years of the uniqueness conjecture. A mathematical journey from irrational numbers to perfect matchings. Cham: Springer (2013; Zbl 1276.00006) Full Text: DOI
Halter-Koch, Franz Quadratic irrationals. An introduction to classical number theory. (English) Zbl 1271.11001 Pure and Applied Mathematics (Boca Raton) 306. Boca Raton, FL: CRC Press (ISBN 978-1-4665-9183-7/hbk; 978-1-4665-9184-4/ebook). xvi, 415 p. (2013). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11R11 11R29 11E16 11A55 11M06 11N05 PDFBibTeX XMLCite \textit{F. Halter-Koch}, Quadratic irrationals. An introduction to classical number theory. Boca Raton, FL: CRC Press (2013; Zbl 1271.11001) Full Text: DOI
Ash, Avner; Gross, Robert Elliptic tales. Curves, counting, and number theory. (English) Zbl 1256.11036 Princeton, NJ: Princeton University Press (ISBN 978-0-691-15119-9/hbk; 978-1-400-84171-4/ebook). xvii, 253 p. (2012). Reviewer: Jan-Hendrik Evertse (Leiden) MSC: 11-01 11G05 11D25 14H52 14G10 PDFBibTeX XMLCite \textit{A. Ash} and \textit{R. Gross}, Elliptic tales. Curves, counting, and number theory. Princeton, NJ: Princeton University Press (2012; Zbl 1256.11036) Full Text: DOI
Wittenberg, Olivier Intersections of two quadrics and pencils of curves of genus 1. (Intersections de deux quadriques et pinceaux de courbes de genre 1.) (French) Zbl 1122.14001 Lecture Notes in Mathematics 1901. Berlin: Springer (ISBN 978-3-540-69137-2/pbk). viii, 218 p. (2007). Reviewer: Boris Kunyavskii (Ramat Gan) MSC: 14-02 11G35 14J20 14J27 14J26 11D25 14G25 14D10 PDFBibTeX XMLCite \textit{O. Wittenberg}, Intersections de deux quadriques et pinceaux de courbes de genre 1. Berlin: Springer (2007; Zbl 1122.14001) Full Text: arXiv
Lemmermeyer, Franz Reciprocity laws. From Euler to Eisenstein. (English) Zbl 0949.11002 Springer Monographs in Mathematics. Berlin: Springer. xix, 487 p. (2000). Reviewer: Hans Opolka (Braunschweig) MSC: 11-03 11A15 01-01 11-01 11R18 11R37 PDFBibTeX XMLCite \textit{F. Lemmermeyer}, Reciprocity laws. From Euler to Eisenstein. Berlin: Springer (2000; Zbl 0949.11002)
Dence, Joseph B.; Dence, Thomas P. Elements of the theory of numbers. (English) Zbl 0932.11001 San Diego, CA: Harcourt/Academic Press. xviii, 517 p. (1999). Reviewer: N.Robbins (San Francisco) MSC: 11-01 11Axx 11P81 11B37 11R11 PDFBibTeX XMLCite \textit{J. B. Dence} and \textit{T. P. Dence}, Elements of the theory of numbers. San Diego, CA: Harcourt/Academic Press (1999; Zbl 0932.11001)
Broberg, Niklas Rational points on cubic surfaces. (English) Zbl 0949.11017 Chalmers University of Technology. The University of Göteborg, Department of Mathematics. Preprint. 38. Göteborg: Chalmers Univ. of Technology and Göteborg University, Department of Mathematics, 18 p. (1999). Reviewer: D.R.Heath-Brown (Oxford) MSC: 11D25 11G35 14G05 11E76 11R47 PDFBibTeX XMLCite \textit{N. Broberg}, Rational points on cubic surfaces. Göteborg: Chalmers Univ. of Technology and Göteborg University, Department of Mathematics (1999; Zbl 0949.11017)
Smart, Nigel P. The algorithmic resolution of Diophantine equations. (English) Zbl 0907.11001 London Mathematical Society Student Texts. 41. Cambridge: Cambridge University Press. xvi, 243 p. (1998). Reviewer: István Gaál (Debrecen) MSC: 11-02 11Y50 11D25 11D57 11D75 11G05 14G05 11G30 11J86 PDFBibTeX XMLCite \textit{N. P. Smart}, The algorithmic resolution of Diophantine equations. Cambridge: Cambridge University Press (1998; Zbl 0907.11001)
Nakagawa, Jin Orders of a quartic field. (English) Zbl 0865.11069 Mem. Am. Math. Soc. 583, 75 p. (1996). Reviewer: R.Mollin (Calgary) MSC: 11R16 11R54 11M41 11N45 PDFBibTeX XMLCite \textit{J. Nakagawa}, Orders of a quartic field. Providence, RI: American Mathematical Society (AMS) (1996; Zbl 0865.11069) Full Text: DOI
Koppenhöfer, David On projective representations of algebras of small rank. (Über projektive Darstellungen von Algebren kleinen Ranges.) (German) Zbl 0869.16009 Tübingen: Univ. Tübingen, Math. Fak. i, 67 S. (1994). Reviewer: I.Gaál (Debrecen) MSC: 16G30 11Y40 11R33 PDFBibTeX XMLCite \textit{D. Koppenhöfer}, Über projektive Darstellungen von Algebren kleinen Ranges. Tübingen: Univ. Tübingen, Math. Fak. (1994; Zbl 0869.16009)
Hetrodt, Georg On a connection between the spectral theory of automorphic functions on the upper half-space and the class numbers of biquadratic number fields. (Über einen Zusammenhang zwischen der Spektraltheorie automorpher Funktionen auf dem oberen Halbraum und den Klassenzahlen biquadratischer Zahlkörper.) (German) Zbl 0847.11030 Schriftenreihe des Mathematischen Instituts der Universität Münster. 3. Serie. 17. Münster: Univ., Math. Inst. 80 p. (1994). Reviewer: J.Elstrodt (Münster) MSC: 11F72 11R29 11R16 PDFBibTeX XMLCite \textit{G. Hetrodt}, Über einen Zusammenhang zwischen der Spektraltheorie automorpher Funktionen auf dem oberen Halbraum und den Klassenzahlen biquadratischer Zahlkörper. Münster: Univ., Math. Inst. (1994; Zbl 0847.11030)
Silverman, Joseph H.; Tate, John Rational points on elliptic curves. (English) Zbl 0752.14034 Undergraduate Texts in Mathematics. New York: Springer-Verlag. x, 281 p. (1992). Reviewer: Gerhard Pfister (Berlin) MSC: 11G05 11-01 14-01 11G15 11D25 14G05 14G15 14H52 PDFBibTeX XMLCite \textit{J. H. Silverman} and \textit{J. Tate}, Rational points on elliptic curves. New York: Springer-Verlag (1992; Zbl 0752.14034)
Fröhlich, A.; Taylor, M. J. Algebraic number theory. (English) Zbl 0744.11001 Cambridge Studies in Advanced Mathematics. 27. Cambridge (UK): Cambridge University Press. xiv, 355 p. (1990). Reviewer: Veikko Ennola (Turku) MSC: 11-01 11Rxx 11R27 11R33 11R29 11D41 11R18 11R42 11D25 11R11 11R16 11R21 PDFBibTeX XMLCite \textit{A. Fröhlich} and \textit{M. J. Taylor}, Algebraic number theory. Cambridge (UK): Cambridge University Press (1990; Zbl 0744.11001)
Hansen, Johan P. Group codes on algebraic curves. (English) Zbl 0619.14018 Math. Gottingensis, Schriftenr. Sonderforschungsbereichs Geom. Anal. 9, 19 p. (1987). Reviewer: E.Ederle MSC: 14H25 14G15 94B05 14-04 94B35 PDFBibTeX XML
Datskovsky, Boris; Wright, David J. Density of discriminants of cubic extensions. (English) Zbl 0619.12005 Math. Gottingensis, Schriftenr. Sonderforschungsbereichs Geom. Anal. 20, 23 p. (1987). Reviewer: J.Hinz MSC: 11R23 11R58 11E12 11R45 11N45 11R16 14G25 11R42 14H05 PDFBibTeX XML
Husemoller, Dale H. [Lawrence, Ruth] Elliptic curves. With an appendix by Ruth Lawrence. (English) Zbl 0605.14032 Graduate Texts in Mathematics, 111. New York etc.: Springer-Verlag. XV, 350 p. DM 110.00 (1987). Reviewer: G. Faltings MSC: 11G05 11-01 11G40 11D25 PDFBibTeX XML
Toussaint, Hans-Joachim Der Algorithmus von Viggo Brun und verwandte Kettenbruch-Entwicklungen. (Viggo Brun’s algorithm and related continued fraction expansions). (German) Zbl 0619.10028 Fakultät für Mathematik und Informatik der Technischen Universität München. 150 S. (1986). Reviewer: F.Schweiger MSC: 11J70 11A55 11R16 11R06 PDFBibTeX XML
Silverman, Joseph H. The arithmetic of elliptic curves. (English) Zbl 0585.14026 Graduate Texts in Mathematics, 106. New York etc.: Springer-Verlag. XII, 400 p. DM 148.00 (1986). Reviewer: R. Gillard MSC: 11G05 11-01 11G07 11G20 11G40 14H45 14G05 14H25 14-01 14H52 11D25 PDFBibTeX XML
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 PDFBibTeX XML
Evertse, J. H. Upper bounds for the numbers of solutions of diophantine equations. (English) Zbl 0517.10016 Mathematical Centre Tracts, 168. Amsterdam: Mathematisch Centrum. v, 125 p. Dfl. 16.50 (1983). Reviewer: A. Pethő MSC: 11D45 11D59 11D25 11D61 11D75 11R27 11-02 PDFBibTeX XML
Sprindzhuk, V. G. Classical diophantine equations in two unknowns. (Классические диофантовы уравнения от двух неизвестных.) (Russian) Zbl 0523.10008 Moskva: “Nauka” Glavnaya Redaktsiya Fiziko-Matematicheskoĭ Literatury. 288 p. R. 2.60 (1982). Reviewer: Ray Phillip Steiner (Bowling Green) MSC: 11Dxx 11-02 11Jxx 11D25 11D41 11D57 11D59 11D61 11D85 11D88 11J86 11R29 11J68 11J81 11J61 PDFBibTeX XML
Schmithals, Bodo Zur Kapitulation der Idealklassen in zyklischen Zahlkörpererweiterungen und Einheitenstruktur in Diederkörpern vom Grad \(2l\). Dissertation. (German) Zbl 0512.12008 Dortmund: Abteilung Mathematik der Universität Dortmund. 129 S. (1982). Reviewer: Franz Halter-Koch (Graz) MSC: 11R18 11R34 11R16 11R27 11R29 11R37 11R21 PDFBibTeX XML
Brentjes, A. J. Multi-dimensional continued fraction algorithms. (English) Zbl 0471.10024 Mathematical Centre Tracts, 145. Amsterdam: Mathematisch Centrum. 183 p. Dfl. 23.10 (1981). MSC: 11J70 11-02 11R27 11R16 11H06 11A55 PDFBibTeX XML
Laska, Michael Die diophantische Gleichung \(x^3 - y^2= \varepsilon(1+i)^m 3^n\) über \(\mathbb Z[i]\) und die Klassifikation gewisser elliptischer Kurven über \(\mathbb Q(i)\). (German) Zbl 0451.10011 Bielefeld: Fakultät für Mathematik der Universität Bielefeld. 154 S. (1980). Reviewer: Roelof J. Stroeker (Rotterdam) MSC: 11D25 11G05 14H52 11Y50 PDFBibTeX XML
Stroeker, Roelof J. Elliptic curves defined over imaginary quadratic number fields. A diophantine approach. (English) Zbl 0342.14014 Amsterdam: Universiteit van Amsterdam. 108 p. (1975). MSC: 11G05 11D25 11-02 14H42 PDFBibTeX XML
Delone, B. N.; Faddeev, D. K. The theory of irrationalities of the third degree. Translated from the Russian by Emma Lehmer and Sue Ann Walker. (English) Zbl 0133.30202 Translations of Mathematical Monographs. 10. Providence, R.I.: American Mathematical Society (AMS). xvi, 509 pp. (1964). MSC: 11-02 11R16 11R27 11R29 11Rxx PDFBibTeX XML
Skolem, Th. Diophantische Gleichungen. (German) Zbl 0018.29302 Ergebnisse der Mathematik und ihrer Grenzgebiete. 5, No. 4. Berlin: Julius Springer. 130 S. (1938). Reviewer: K. Mahler (Manchester) MSC: 11Dxx 11-02 11D04 11D09 11D25 11D57 11D85 11E25 11G30 14G05 14G25 14H25 PDFBibTeX XML
Ljunggren, Wilhelm Einige Eigenschaften der Einheiten reeller quadratischer und rein-biquadratischer Zahlkörper mit Anwendung auf die Lösung einer Klasse unbestimmter Gleichungen vierten Grades. (German) Zbl 0016.00802 Skr. Norske Vid.-Akad., Oslo 1936, No. 12, 1-73 (1936). Reviewer: Salomon Lubelski (Warszawa) MSC: 11R11 11R27 11D25 PDFBibTeX XML
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 PDFBibTeX XML
Sommer, J. Lectures on Number Theory. An Introduction to Algebraic Number Fields. (Vorlesungen über Zahlentheorie. Einführung in die Theorie der algebraischen Zahlkröper.) (German) JFM 38.0221.01 Berlin u. Leipzig: B. G. Teubner. VI u. 361 S. (1907). Reviewer: Fueter, Prof. (Basel) MSC: 11-01 11R11 11R16 PDFBibTeX XML Full Text: Link
Minkowski, H. Diophantine approximations. An introduction to number theory. (Diophantische Approximationen. Eine Einführung in die Zahlentheorie.) (German) JFM 38.0220.15 Mathematische Vorlesungen an der Universität Göttingen. II. Leipzig: B. G. Teubner. viii, 235 S. Mit 82 Fig. (1907). Reviewer: Fueter, Prof. (Basel) MSC: 11-01 11Jxx 11R16 11R27 11R29 PDFBibTeX XML
Gmeiner, J. A. On integers in the rational domain of the fifth roots of unity. (Ueber die ganzen Zahlen im Rationalitätsgebiete der fünften Einheitswurzeln.) (German) JFM 27.0159.03 Programm des Staats-Gymn. in Pola. VI. Jahrgang. 24 S. (1896). Reviewer: Haussner, Prof. (Giessen) MSC: 11R16 11R18 PDFBibTeX XML