Park, Choonkil; Ghaemi, Mohammad Bagher; Majani, Hamid; Gordji, Madjid Eshaghi; Najati, Abbas Fixed points and approximately heptic mappings in non-Archimedean normed spaces. (English) Zbl 1381.39031 Adv. Difference Equ. 2013, Paper No. 209, 10 p. (2013). MSC: 39B82 39B52 46S10 39B72 39B55 PDFBibTeX XMLCite \textit{C. Park} et al., Adv. Difference Equ. 2013, Paper No. 209, 10 p. (2013; Zbl 1381.39031) Full Text: DOI
Moody, Dustin; Shamsi Zargar, Arman On integer solutions of \(x^4+y^4-2z^4-2w^4=0\). (English) Zbl 1310.11037 Notes Number Theory Discrete Math. 19, No. 1, 37-43 (2013). MSC: 11D25 11G05 PDFBibTeX XMLCite \textit{D. Moody} and \textit{A. Shamsi Zargar}, Notes Number Theory Discrete Math. 19, No. 1, 37--43 (2013; Zbl 1310.11037) Full Text: Link
Aguilar-Zavoznik, Alejandro; Pineda-Ruelas, Mario Ramification of 2 in quadratic extensions over some pure quartic fields. (English) Zbl 1303.11121 Int. J. Algebra 7, No. 9-12, 487-508 (2013). MSC: 11R11 11R21 11Y40 PDFBibTeX XMLCite \textit{A. Aguilar-Zavoznik} and \textit{M. Pineda-Ruelas}, Int. J. Algebra 7, No. 9--12, 487--508 (2013; Zbl 1303.11121) Full Text: DOI Link
Lur’e, B. B. On a method of solving Diophantine equations. (English. Russian original) Zbl 1302.11011 J. Math. Sci., New York 192, No. 2, 232-233 (2013); translation from Zap. Nauchn. Sem. POMI 400, 189-192 (2012). MSC: 11D25 11G05 PDFBibTeX XMLCite \textit{B. B. Lur'e}, J. Math. Sci., New York 192, No. 2, 232--233 (2013; Zbl 1302.11011); translation from Zap. Nauchn. Sem. POMI 400, 189--192 (2012) Full Text: DOI
Ulas, Maciej A note on Diophantine systems involving three symmetric polynomials. (English) Zbl 1295.11028 J. Number Theory 133, No. 10, 3283-3295 (2013). MSC: 11D25 11D72 11G05 11C08 PDFBibTeX XMLCite \textit{M. Ulas}, J. Number Theory 133, No. 10, 3283--3295 (2013; Zbl 1295.11028) Full Text: DOI arXiv
Luo, Bin; Wu, Yuhai Phase portraits of a Z5-equivariant quartic Hamiltonian system. (English) Zbl 1299.34120 Ann. Differ. Equations 29, No. 4, 438-442 (2013). MSC: 34C07 34C23 34C37 37G15 37J45 37J15 PDFBibTeX XMLCite \textit{B. Luo} and \textit{Y. Wu}, Ann. Differ. Equations 29, No. 4, 438--442 (2013; Zbl 1299.34120)
Preu, Thomas Example of a transcendental 3-torsion Brauer-Manin obstruction on a diagonal quartic surface. (English) Zbl 1290.14015 Skorobogatov, Alexei N. (ed.), Torsors, étale homotopy and applications to rational points. Lecture notes of mini-courses presented at the workshop “Torsors: theory and applications”, Edinburgh, UK, January 10–14, 2011 and at the study group organised in Imperial College, London, UK in autumn 2010. Cambridge: Cambridge University Press (ISBN 978-1-107-61612-7/pbk; 978-1-139-52535-0/ebook). London Mathematical Society Lecture Note Series 405, 447-459 (2013). MSC: 14G05 11G35 11D25 14F22 PDFBibTeX XMLCite \textit{T. Preu}, Lond. Math. Soc. Lect. Note Ser. 405, 447--459 (2013; Zbl 1290.14015)
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
Ren, Zhi A Diophantine system concerning sums of cubes. (English) Zbl 1285.11058 J. Integer Seq. 16, No. 7, Article 13.7.8, 11 p. (2013). MSC: 11D25 11D72 11G05 PDFBibTeX XMLCite \textit{Z. Ren}, J. Integer Seq. 16, No. 7, Article 13.7.8, 11 p. (2013; Zbl 1285.11058) Full Text: EMIS
Kostra, Juraj; Krčmarský, David Note on sums of units in real cubic fields. (English) Zbl 1362.11090 Tatra Mt. Math. Publ. 56, 87-92 (2013). MSC: 11R27 11R04 11R16 PDFBibTeX XMLCite \textit{J. Kostra} and \textit{D. Krčmarský}, Tatra Mt. Math. Publ. 56, 87--92 (2013; Zbl 1362.11090) Full Text: DOI Link
Gu, Xiuchuan The positive integral points on a sort of elliptic curve. (Chinese. English summary) Zbl 1289.11041 J. Math., Wuhan Univ. 33, No. 1, 113-119 (2013). MSC: 11G05 11D25 PDFBibTeX XMLCite \textit{X. Gu}, J. Math., Wuhan Univ. 33, No. 1, 113--119 (2013; Zbl 1289.11041)
Anderson, Jacqueline; Balakrishnan, Jennifer S.; Lauter, Kristin; Park, Jennifer; Viray, Bianca Comparing arithmetic intersection formulas for denominators of Igusa class polynomials. (English) Zbl 1285.11088 David, Chantal (ed.) et al., Women in numbers 2: Research directions in number theory. Second BIRS workshop WIN2, Banff International Research Station, Banff, Canada, November 6–11, 2011. Providence, RI: American Mathematical Society (AMS); Montreal: Centre de Recherches Mathématiques (CRM) (ISBN 978-1-4704-1022-3/pbk; 978-1-4704-1440-5/ebook). Contemporary Mathematics 606. Centre de Recherches Mathématiques Proceedings, 65-82 (2013). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11G15 11R11 11R16 11R47 PDFBibTeX XMLCite \textit{J. Anderson} et al., Contemp. Math. 606, 65--82 (2013; Zbl 1285.11088) Full Text: arXiv
Roblot, Xavier-François Index formulae for stark units and their solutions. (English) Zbl 1284.11149 Pac. J. Math. 266, No. 2, 391-422 (2013). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R27 11R29 11R42 PDFBibTeX XMLCite \textit{X.-F. Roblot}, Pac. J. Math. 266, No. 2, 391--422 (2013; Zbl 1284.11149) Full Text: DOI arXiv
Mayer, Daniel C. The distribution of second \(p\)-class groups on coclass graphs. (English. French summary) Zbl 1292.11126 J. Théor. Nombres Bordx. 25, No. 2, 401-456 (2013). Reviewer: Bouchaïb Sodaïgui (Valenciennes) MSC: 11R29 11R37 11R11 11R16 11R20 20D15 PDFBibTeX XMLCite \textit{D. C. Mayer}, J. Théor. Nombres Bordx. 25, No. 2, 401--456 (2013; Zbl 1292.11126) Full Text: DOI arXiv
Lee, Jun Ho Class number one criterion for some non-normal totally real cubic fields. (English) Zbl 1282.11149 Taiwanese J. Math. 17, No. 3, 981-989 (2013). MSC: 11R42 11R16 11R29 PDFBibTeX XMLCite \textit{J. H. Lee}, Taiwanese J. Math. 17, No. 3, 981--989 (2013; Zbl 1282.11149) Full Text: DOI arXiv Link
Kozuma, Rintaro Elliptic curves related to cyclic cubic extensions. II. (English) Zbl 1367.11056 Comment. Math. Univ. St. Pauli 62, No. 1, 31-58 (2013). Reviewer: Andrea Bandini (Parma) MSC: 11G05 11G07 11R16 PDFBibTeX XMLCite \textit{R. Kozuma}, Comment. Math. Univ. St. Pauli 62, No. 1, 31--58 (2013; Zbl 1367.11056) Full Text: Link
Lampakis, Elias An other proof of the insolubility of Fermat’s cubic equation in Eisenstein’s ring. (English) Zbl 1343.11041 J. Indones. Math. Soc. 19, No. 1, 61-66 (2013). MSC: 11D41 11D25 11G05 PDFBibTeX XMLCite \textit{E. Lampakis}, J. Indones. Math. Soc. 19, No. 1, 61--66 (2013; Zbl 1343.11041) Full Text: DOI
Huang, Wentao; Chen, Aiyong; Xu, Qiujin Bifurcation of limit cycles and isochronous centers for a quartic system. (English) Zbl 1277.34044 Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 10, Article ID 1350172, 10 p. (2013). MSC: 34C23 34C05 34C25 34C07 PDFBibTeX XMLCite \textit{W. Huang} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 10, Article ID 1350172, 10 p. (2013; Zbl 1277.34044) Full Text: DOI
Yang, Hai; Fu, Ruiqin The integral points on elliptic curves \(y^2=x^3+(36n^2 -9)x-2(36n^2-5)\). (English) Zbl 1289.11034 Czech. Math. J. 63, No. 2, 375-383 (2013). Reviewer: Attila Bérczes (Debrecen) MSC: 11D25 11G05 PDFBibTeX XMLCite \textit{H. Yang} and \textit{R. Fu}, Czech. Math. J. 63, No. 2, 375--383 (2013; Zbl 1289.11034) Full Text: DOI
Swarbrick Jones, Mike Weak approximation for cubic hypersurfaces of large dimension. (English) Zbl 1368.11058 Algebra Number Theory 7, No. 6, 1353-1363 (2013). MSC: 11G35 11D25 11D72 11P55 14G25 PDFBibTeX XMLCite \textit{M. Swarbrick Jones}, Algebra Number Theory 7, No. 6, 1353--1363 (2013; Zbl 1368.11058) Full Text: DOI arXiv
Lemmermeyer, Franz Why is the class number of \(\mathbb {Q}(\root 3\of {11})\) even? (English) Zbl 1274.11162 Math. Bohem. 138, No. 2, 149-163 (2013). Reviewer: Radan Kučera (Brno) MSC: 11R16 11R29 11G05 PDFBibTeX XMLCite \textit{F. Lemmermeyer}, Math. Bohem. 138, No. 2, 149--163 (2013; Zbl 1274.11162) Full Text: arXiv Link
Fujita, Yasutsugu; Terai, Nobuhiro Generators and integer points on the elliptic curve \(y^2=x^3-nx\). (English) Zbl 1310.11036 Acta Arith. 160, No. 4, 333-348 (2013). MSC: 11D25 11G05 14G05 11G50 PDFBibTeX XMLCite \textit{Y. Fujita} and \textit{N. Terai}, Acta Arith. 160, No. 4, 333--348 (2013; Zbl 1310.11036) Full Text: DOI
Bennett, Michael A. Integral points on congruent number curves. (English) Zbl 1318.11047 Int. J. Number Theory 9, No. 6, 1619-1640 (2013). MSC: 11D25 11G05 PDFBibTeX XMLCite \textit{M. A. Bennett}, Int. J. Number Theory 9, No. 6, 1619--1640 (2013; Zbl 1318.11047) Full Text: DOI
Krenn, Daniel; Thuswaldner, Jörg; Ziegler, Volker On linear combinations of units with bounded coefficients and double-base digit expansions. (English) Zbl 1325.11119 Monatsh. Math. 171, No. 3-4, 377-394 (2013). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R27 11A63 11A67 11R04 11R16 11T99 11Y16 PDFBibTeX XMLCite \textit{D. Krenn} et al., Monatsh. Math. 171, No. 3--4, 377--394 (2013; Zbl 1325.11119) Full Text: DOI arXiv
Swinnerton-Dyer, H. P. F. Density of rational points on certain surfaces. (English) Zbl 1277.11070 Algebra Number Theory 7, No. 4, 835-851 (2013). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11G35 14G05 11D25 PDFBibTeX XMLCite \textit{H. P. F. Swinnerton-Dyer}, Algebra Number Theory 7, No. 4, 835--851 (2013; Zbl 1277.11070) Full Text: DOI
Naskrȩcki, Bartosz Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples. (English) Zbl 1279.14040 Acta Arith. 160, No. 2, 159-183 (2013). Reviewer: Andrea Bandini (Parma) MSC: 14H52 11G05 11D25 11D45 PDFBibTeX XMLCite \textit{B. Naskrȩcki}, Acta Arith. 160, No. 2, 159--183 (2013; Zbl 1279.14040) Full Text: DOI arXiv
MacLeod, Allan J. Computation of perfect “almost-cuboids”. (English) Zbl 1338.11044 Glas. Mat., III. Ser. 48, No. 1, 23-29 (2013). Reviewer: Andrej Dujella (Zagreb) MSC: 11D25 11G05 11Y50 PDFBibTeX XMLCite \textit{A. J. MacLeod}, Glas. Mat., III. Ser. 48, No. 1, 23--29 (2013; Zbl 1338.11044) Full Text: DOI
Hooley, Christopher On nonary cubic forms. IV. (English) Zbl 1370.11118 J. Reine Angew. Math. 680, 23-39 (2013). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11P55 11D25 11D72 11E76 11G35 14G05 14J17 14J20 PDFBibTeX XMLCite \textit{C. Hooley}, J. Reine Angew. Math. 680, 23--39 (2013; Zbl 1370.11118) 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)
Woo, Sung Sik Cubic formula and cubic curves. (English) Zbl 1328.11033 Commun. Korean Math. Soc. 28, No. 2, 209-224 (2013). MSC: 11D25 11G05 14G05 PDFBibTeX XMLCite \textit{S. S. Woo}, Commun. Korean Math. Soc. 28, No. 2, 209--224 (2013; Zbl 1328.11033) Full Text: DOI Link
Mukhamedov, F. M.; Omirov, B. A.; Saburov, M. Kh.; Masutova, K. K. Solvability of cubic equations in \(p\)-adic integers \((p>3)\). (English. Russian original) Zbl 1294.11205 Sib. Math. J. 54, No. 3, 501-516 (2013); translation from Sib. Mat. Zh. 54, No. 3, 637-654 (2013). Reviewer: Denis Ibadula (Constanta) MSC: 11S05 11D25 11D88 PDFBibTeX XMLCite \textit{F. M. Mukhamedov} et al., Sib. Math. J. 54, No. 3, 501--516 (2013; Zbl 1294.11205); translation from Sib. Mat. Zh. 54, No. 3, 637--654 (2013) Full Text: DOI
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
Morra, Anna An algorithm to compute relative cubic fields. (English) Zbl 1360.11147 Math. Comput. 82, No. 284, 2343-2361 (2013). MSC: 11Y40 11R16 PDFBibTeX XMLCite \textit{A. Morra}, Math. Comput. 82, No. 284, 2343--2361 (2013; Zbl 1360.11147) Full Text: DOI arXiv
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
Lee, Jung Rye; Park, Choonkil; Cho, Yeol Je; Shin, Dong Yun Orthogonal stability of a cubic-quartic functional equation in non-Archimedean spaces. (English) Zbl 1277.39042 J. Comput. Anal. Appl. 15, No. 3, 572-583 (2013). Reviewer: Jacek Chmieliński (Kraków) MSC: 39B82 39B55 39B52 47S10 PDFBibTeX XMLCite \textit{J. R. Lee} et al., J. Comput. Anal. Appl. 15, No. 3, 572--583 (2013; Zbl 1277.39042)
Elsenhans, Andreas-Stephan; Jahnel, Jörg On the computation of the Picard group for certain singular quartic surfaces. (English) Zbl 1317.14086 Math. Slovaca 63, No. 2, 215-228 (2013). Reviewer: Ronald van Luijk (Leiden) MSC: 14J28 14G05 14C22 14J20 PDFBibTeX XMLCite \textit{A.-S. Elsenhans} and \textit{J. Jahnel}, Math. Slovaca 63, No. 2, 215--228 (2013; Zbl 1317.14086) Full Text: DOI
González-Jiménez, Enrique; Tornero, José M. Markoff-Rosenberger triples in arithmetic progression. (English) Zbl 1272.11044 J. Symb. Comput. 53, 53-63 (2013). Reviewer: Gerhard Rosenberger (Hamburg) MSC: 11D25 20H10 PDFBibTeX XMLCite \textit{E. González-Jiménez} and \textit{J. M. Tornero}, J. Symb. Comput. 53, 53--63 (2013; Zbl 1272.11044) Full Text: DOI arXiv
Zhang, Yong; Cai, Tianxin \(N\)-tuples of positive integers with the same sum and the same product. (English) Zbl 1275.11058 Math. Comput. 82, No. 281, 617-623 (2013). MSC: 11D25 11D72 11G05 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{T. Cai}, Math. Comput. 82, No. 281, 617--623 (2013; Zbl 1275.11058) Full Text: DOI
Bennett, Michael A.; Dahmen, Sander R. Klein forms and the generalized superelliptic equation. (English) Zbl 1321.11059 Ann. Math. (2) 177, No. 1, 171-239 (2013). MSC: 11G05 11F80 11D25 11D59 PDFBibTeX XMLCite \textit{M. A. Bennett} and \textit{S. R. Dahmen}, Ann. Math. (2) 177, No. 1, 171--239 (2013; Zbl 1321.11059) Full Text: DOI
Fieker, Claus; Gaál, István; Pohst, Michael On computing integral points of a Mordell curve over rational function fields in characteristic \(>3\). (English) Zbl 1309.11088 J. Number Theory 133, No. 2, 738-750 (2013). MSC: 11Y50 11D25 11D61 11G05 PDFBibTeX XMLCite \textit{C. Fieker} et al., J. Number Theory 133, No. 2, 738--750 (2013; Zbl 1309.11088) Full Text: DOI
Jeon, Daeyeol; Kim, Chang Heon; Lee, Yoonjin Infinite families of elliptic curves over dihedral quartic number fields. (English) Zbl 1268.11077 J. Number Theory 133, No. 1, 115-122 (2013). MSC: 11G05 11G18 PDFBibTeX XMLCite \textit{D. Jeon} et al., J. Number Theory 133, No. 1, 115--122 (2013; Zbl 1268.11077) Full Text: DOI
Leriche, Amandine Cubic, quartic and sextic Pólya fields. (English) Zbl 1296.11136 J. Number Theory 133, No. 1, 59-71 (2013). MSC: 11R16 11R20 11R04 13F20 PDFBibTeX XMLCite \textit{A. Leriche}, J. Number Theory 133, No. 1, 59--71 (2013; Zbl 1296.11136) Full Text: DOI
Nguyen, Lan Finiteness of the Tate-Shafarevich Groups for Elliptic Curves over the Field of Rational Numbers. arXiv:1309.7675 Preprint, arXiv:1309.7675 [math.NT] (2013). MSC: 11C08 11D09 11D25 11G05 11G07 11Y16 BibTeX Cite \textit{L. Nguyen}, ``Finiteness of the Tate-Shafarevich Groups for Elliptic Curves over the Field of Rational Numbers'', Preprint, arXiv:1309.7675 [math.NT] (2013) Full Text: arXiv OA License
Herman, P. Edward On Patterson’s Conjecture: Sums of Quartic Exponential Sums. arXiv:1305.1243 Preprint, arXiv:1305.1243 [math.NT] (2013). MSC: 11D25 11F70 11F72 11L05 11L07 BibTeX Cite \textit{P. E. Herman}, ``On Patterson's Conjecture: Sums of Quartic Exponential Sums'', Preprint, arXiv:1305.1243 [math.NT] (2013) Full Text: arXiv OA License
Ramsden, John; Sharipov, Ruslan Two and three descent for elliptic curves associated with perfect cuboids. arXiv:1303.0765 Preprint, arXiv:1303.0765 [math.NT] (2013). MSC: 11G05 14H52 11D25 11D72 BibTeX Cite \textit{J. Ramsden} and \textit{R. Sharipov}, ``Two and three descent for elliptic curves associated with perfect cuboids'', Preprint, arXiv:1303.0765 [math.NT] (2013) Full Text: arXiv OA License