DeMarco, Laura; Mavraki, Niki Myrto Variation of canonical height for Fatou points on \(\mathbb{P}^1\). (English) Zbl 1511.37117 J. Reine Angew. Math. 795, 183-220 (2023). MSC: 37P40 37P50 37P30 11G50 PDF BibTeX XML Cite \textit{L. DeMarco} and \textit{N. M. Mavraki}, J. Reine Angew. Math. 795, 183--220 (2023; Zbl 1511.37117) Full Text: DOI arXiv
Gauthier, Thomas; Vigny, Gabriel The geometric dynamical Northcott property for regular polynomial automorphisms of the affine plane. (English) Zbl 07714404 Bull. Soc. Math. Fr. 150, No. 4, 677-698 (2022). MSC: 37P15 37P30 PDF BibTeX XML Cite \textit{T. Gauthier} and \textit{G. Vigny}, Bull. Soc. Math. Fr. 150, No. 4, 677--698 (2022; Zbl 07714404) Full Text: DOI arXiv
Xie, Junyi; Yuan, Xinyi Geometric Bogomolov conjecture in arbitrary characteristics. (English) Zbl 1508.14028 Invent. Math. 229, No. 2, 607-637 (2022). Reviewer: Nikolaj M. Glazunov (Kyjiw) MSC: 14G40 14G05 11G50 PDF BibTeX XML Cite \textit{J. Xie} and \textit{X. Yuan}, Invent. Math. 229, No. 2, 607--637 (2022; Zbl 1508.14028) Full Text: DOI arXiv
Corvaja, Pietro; Demeio, Julian; Masser, David; Zannier, Umberto On the torsion values for sections of an elliptic scheme. (English) Zbl 1485.14085 J. Reine Angew. Math. 782, 1-41 (2022). Reviewer: Matthias Schütt (Hannover) MSC: 14K15 11G50 11J68 11G05 11J99 PDF BibTeX XML Cite \textit{P. Corvaja} et al., J. Reine Angew. Math. 782, 1--41 (2022; Zbl 1485.14085) Full Text: DOI arXiv
Naccarato, Francesco Counting rational points on elliptic curves with a rational 2-torsion point. (English) Zbl 1483.11117 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 32, No. 3, 499-509 (2021). MSC: 11G05 PDF BibTeX XML Cite \textit{F. Naccarato}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 32, No. 3, 499--509 (2021; Zbl 1483.11117) Full Text: DOI arXiv
Rout, Sudhansu Sekhar; Juyal, Abhishek The Mordell-Weil bases for the elliptic curve \(y^2=x^3-m^2x+m^2\). (English) Zbl 07442479 Czech. Math. J. 71, No. 4, 1133-1147 (2021). MSC: 11G05 11D59 PDF BibTeX XML Cite \textit{S. S. Rout} and \textit{A. Juyal}, Czech. Math. J. 71, No. 4, 1133--1147 (2021; Zbl 07442479) Full Text: DOI
Okazaki, M. Canonical heights on Pell conics over number fields. (English) Zbl 1454.11124 Armen. J. Math. 12, Paper No. 5, 9 p. (2020). MSC: 11G50 11D09 14G05 14H50 20G30 PDF BibTeX XML Cite \textit{M. Okazaki}, Armen. J. Math. 12, Paper No. 5, 9 p. (2020; Zbl 1454.11124) Full Text: Link
Müller, Susanne \(F\)-pure threshold and height of quasihomogeneous polynomials. (English) Zbl 1453.13022 J. Commut. Algebra 12, No. 4, 559-572 (2020). MSC: 13A35 14B05 32S35 PDF BibTeX XML Cite \textit{S. Müller}, J. Commut. Algebra 12, No. 4, 559--572 (2020; Zbl 1453.13022) Full Text: DOI arXiv Euclid
DeMarco, Laura; Mavraki, Niki Myrto Variation of canonical height and equidistribution. (English) Zbl 1461.11102 Am. J. Math. 142, No. 2, 443-473 (2020). Reviewer: Riccardo Pengo (Lyon) MSC: 11G50 14G40 37P05 PDF BibTeX XML Cite \textit{L. DeMarco} and \textit{N. M. Mavraki}, Am. J. Math. 142, No. 2, 443--473 (2020; Zbl 1461.11102) Full Text: DOI arXiv
Mello, Jorge The dynamical and arithmetical degrees for eigensystems of rational self-maps. (English) Zbl 1445.37079 Bull. Braz. Math. Soc. (N.S.) 51, No. 2, 569-596 (2020). MSC: 37P30 14E05 37C35 PDF BibTeX XML Cite \textit{J. Mello}, Bull. Braz. Math. Soc. (N.S.) 51, No. 2, 569--596 (2020; Zbl 1445.37079) Full Text: DOI arXiv
Kawaguchi, Shu; Silverman, Joseph H. Addendum to “Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties”. (English) Zbl 1433.37085 Trans. Am. Math. Soc. 373, No. 3, 2253 (2020). MSC: 37P30 37P15 37P55 11G10 11G50 PDF BibTeX XML Cite \textit{S. Kawaguchi} and \textit{J. H. Silverman}, Trans. Am. Math. Soc. 373, No. 3, 2253 (2020; Zbl 1433.37085) Full Text: DOI
Mello, Jorge On variation of dynamical canonical heights for semigroups of morphisms. (English) Zbl 1434.37055 J. Pure Appl. Algebra 224, No. 3, 1195-1204 (2020). MSC: 37P55 11G50 37P30 PDF BibTeX XML Cite \textit{J. Mello}, J. Pure Appl. Algebra 224, No. 3, 1195--1204 (2020; Zbl 1434.37055) Full Text: DOI
Ingram, Patrick Canonical heights and preperiodic points for certain weighted homogeneous families of polynomials. (English) Zbl 1456.37108 Int. Math. Res. Not. 2019, No. 15, 4859-4879 (2019). MSC: 37P05 37P30 11G50 PDF BibTeX XML Cite \textit{P. Ingram}, Int. Math. Res. Not. 2019, No. 15, 4859--4879 (2019; Zbl 1456.37108) Full Text: DOI arXiv
Fujita, Yasutsugu; Nara, Tadahisa Generators and integral points on certain quartic curves. (English) Zbl 1446.11108 Glas. Mat., III. Ser. 54, No. 2, 321-343 (2019). Reviewer: Noburo Ishii (Kyoto) MSC: 11G05 11D25 11G50 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{T. Nara}, Glas. Mat., III. Ser. 54, No. 2, 321--343 (2019; Zbl 1446.11108) Full Text: DOI Link
Le Boudec, Pierre A statistical view on the conjecture of Lang about the canonical height on elliptic curves. (English) Zbl 1473.11137 Trans. Am. Math. Soc. 372, No. 12, 8347-8361 (2019). MSC: 11G50 11G05 14G05 11D45 PDF BibTeX XML Cite \textit{P. Le Boudec}, Trans. Am. Math. Soc. 372, No. 12, 8347--8361 (2019; Zbl 1473.11137) Full Text: DOI arXiv
Müller, J. Steffen; Stumpe, Corinna Archimedean local height differences on elliptic curves. (English) Zbl 1453.11087 Acta Arith. 190, No. 3, 293-303 (2019). MSC: 11G50 14G05 11G05 11G07 PDF BibTeX XML Cite \textit{J. S. Müller} and \textit{C. Stumpe}, Acta Arith. 190, No. 3, 293--303 (2019; Zbl 1453.11087) Full Text: DOI arXiv Link
Mello, Jorge Canonical heights and monomial maps: on effective lower bounds for points with dense orbit. (English) Zbl 1436.37102 J. Number Theory 205, 321-339 (2019). MSC: 37P30 37P55 11G50 14E05 PDF BibTeX XML Cite \textit{J. Mello}, J. Number Theory 205, 321--339 (2019; Zbl 1436.37102) Full Text: DOI arXiv
Shibata, Takahiro Ample canonical heights for endomorphisms on projective varieties. (English) Zbl 1442.37124 J. Math. Soc. Japan 71, No. 2, 599-634 (2019). MSC: 37P30 14G05 PDF BibTeX XML Cite \textit{T. Shibata}, J. Math. Soc. Japan 71, No. 2, 599--634 (2019; Zbl 1442.37124) Full Text: DOI arXiv Euclid
De Marco, Laura; Ghioca, Dragos Rationality of dynamical canonical height. (English) Zbl 1471.37085 Ergodic Theory Dyn. Syst. 39, No. 9, 2507-2540 (2019). MSC: 37P40 37P30 14H52 PDF BibTeX XML Cite \textit{L. De Marco} and \textit{D. Ghioca}, Ergodic Theory Dyn. Syst. 39, No. 9, 2507--2540 (2019; Zbl 1471.37085) Full Text: DOI arXiv
Looper, Nicole A lower bound on the canonical height for polynomials. (English) Zbl 1470.11187 Math. Ann. 373, No. 3-4, 1057-1074 (2019). MSC: 11G50 37P30 37P45 37P15 PDF BibTeX XML Cite \textit{N. Looper}, Math. Ann. 373, No. 3--4, 1057--1074 (2019; Zbl 1470.11187) Full Text: DOI arXiv
Ingram, Patrick Canonical heights for correspondences. (English) Zbl 1410.37094 Trans. Am. Math. Soc. 371, No. 2, 1003-1027 (2019). Reviewer: Franco Vivaldi (London) MSC: 37P30 37F05 PDF BibTeX XML Cite \textit{P. Ingram}, Trans. Am. Math. Soc. 371, No. 2, 1003--1027 (2019; Zbl 1410.37094) Full Text: DOI arXiv
Habegger, Philipp; Ih, Su-ion Distribution of integral division points on the algebraic torus. (English) Zbl 1416.11113 Trans. Am. Math. Soc. 371, No. 1, 357-386 (2019). Reviewer: Michel Waldschmidt (Paris) MSC: 11G50 11J61 11J71 11J86 11L15 14G25 14G40 20G30 37P05 37P35 PDF BibTeX XML Cite \textit{P. Habegger} and \textit{S.-i. Ih}, Trans. Am. Math. Soc. 371, No. 1, 357--386 (2019; Zbl 1416.11113) Full Text: DOI
Fujita, Yasutsugu; Nara, Tadahisa The Mordell-Weil bases for the elliptic curve of the form \(y^2 = x^3-m^2x + n^2\). (English) Zbl 1413.11081 Publ. Math. Debr. 92, No. 1-2, 79-99 (2018). MSC: 11G05 11D59 11G50 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{T. Nara}, Publ. Math. Debr. 92, No. 1--2, 79--99 (2018; Zbl 1413.11081) Full Text: DOI arXiv
Winckler, Bruno Lehmer’s problem on elliptic curves with complex multiplications. (Problème de Lehmer sur les courbes elliptiques à multiplications complexes.) (French. English summary) Zbl 1422.11145 Acta Arith. 182, No. 4, 347-396 (2018). MSC: 11G50 14G40 11M06 PDF BibTeX XML Cite \textit{B. Winckler}, Acta Arith. 182, No. 4, 347--396 (2018; Zbl 1422.11145) Full Text: DOI
Sha, Min; Shparlinski, Igor E. Effective results on linear dependence for elliptic curves. (English) Zbl 1450.11055 Pac. J. Math. 295, No. 1, 123-144 (2018). Reviewer: Maciej Ulas (Kraków) MSC: 11G05 11G50 PDF BibTeX XML Cite \textit{M. Sha} and \textit{I. E. Shparlinski}, Pac. J. Math. 295, No. 1, 123--144 (2018; Zbl 1450.11055) Full Text: DOI arXiv
Stoll, Michael An explicit theory of heights for hyperelliptic Jacobians of genus three. (English) Zbl 1406.14023 Böckle, Gebhard (ed.) et al., Algorithmic and experimental methods in algebra, geometry, and number theory. Cham: Springer (ISBN 978-3-319-70565-1/hbk; 978-3-319-70566-8/ebook). 665-715 (2017). Reviewer: V. V. Chueshev (Kemerovo) MSC: 14H40 11G10 11G50 PDF BibTeX XML Cite \textit{M. Stoll}, in: Algorithmic and experimental methods in algebra, geometry, and number theory. Cham: Springer. 665--715 (2017; Zbl 1406.14023) Full Text: DOI arXiv
Yamaki, Kazuhiko Survey on the geometric Bogomolov conjecture. (English. French summary) Zbl 1404.14028 Actes de la conférence “Non-Archimedean analytic geometry: theory and practice”. Besançon: Presses Universitaires de Franche-Comté (ISBN 978-2-84867-608-1/pbk). Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2017, 1, 137-193 (2017). MSC: 14G40 11G50 14K05 37P30 PDF BibTeX XML Cite \textit{K. Yamaki}, Publ. Math. Besançon, Algèbre Théor. Nombres 2017, 137--193 (2017; Zbl 1404.14028) Full Text: arXiv
Biesel, Owen; Holmes, David; de Jong, Robin Néron models and the height jump divisor. (English) Zbl 1374.14023 Trans. Am. Math. Soc. 369, No. 12, 8685-8723 (2017). Reviewer: Roberto Dvornicich (Pisa) MSC: 14H10 11G50 14G40 14K15 PDF BibTeX XML Cite \textit{O. Biesel} et al., Trans. Am. Math. Soc. 369, No. 12, 8685--8723 (2017; Zbl 1374.14023) Full Text: DOI arXiv
Tokgoz, G.; Sakalli, I. Stationary scalar clouds around maximally rotating linear dilaton black holes. (English) Zbl 1367.83062 Classical Quantum Gravity 34, No. 12, Article ID 125007, 11 p. (2017). MSC: 83C57 83C05 PDF BibTeX XML Cite \textit{G. Tokgoz} and \textit{I. Sakalli}, Classical Quantum Gravity 34, No. 12, Article ID 125007, 11 p. (2017; Zbl 1367.83062) Full Text: DOI arXiv
Wells, Elliot Computing canonical heights on the projective line with no factorization. (English) Zbl 1392.37114 Math. Comput. 86, No. 308, 3019-3029 (2017). MSC: 37P30 11G50 11Y16 PDF BibTeX XML Cite \textit{E. Wells}, Math. Comput. 86, No. 308, 3019--3029 (2017; Zbl 1392.37114) Full Text: DOI arXiv
Drungilas, Paulius; Eitmantis, Jaunius Height reducing property of certain cubic algebraic integers. (English) Zbl 1409.11089 Šiauliai Math. Semin. 11(19), 15-23 (2016). MSC: 11R11 11R04 PDF BibTeX XML Cite \textit{P. Drungilas} and \textit{J. Eitmantis}, Šiauliai Math. Semin. 11(19), 15--23 (2016; Zbl 1409.11089)
Müller, Jan Steffen; Stoll, Michael Canonical heights on genus-2 Jacobians. (English) Zbl 1383.11089 Algebra Number Theory 10, No. 10, 2153-2234 (2016). Reviewer: Patrick Ingram (Toronto) MSC: 11G50 11G30 11G10 14G40 14Q05 14G05 PDF BibTeX XML Cite \textit{J. S. Müller} and \textit{M. Stoll}, Algebra Number Theory 10, No. 10, 2153--2234 (2016; Zbl 1383.11089) Full Text: DOI arXiv
DeMarco, Laura Bifurcations, intersections, and heights. (English) Zbl 1391.37076 Algebra Number Theory 10, No. 5, 1031-1056 (2016). MSC: 37P30 37F45 11G05 PDF BibTeX XML Cite \textit{L. DeMarco}, Algebra Number Theory 10, No. 5, 1031--1056 (2016; Zbl 1391.37076) Full Text: DOI arXiv
Voutier, Paul; Yabuta, Minoru Lang’s conjecture and sharp height estimates for the elliptic curves \(y^{2}=x^{3}+b\). (English) Zbl 1348.11045 Acta Arith. 173, No. 3, 197-224 (2016). Reviewer: Cyril Hugounenq (Versailles) MSC: 11G05 11G50 PDF BibTeX XML Cite \textit{P. Voutier} and \textit{M. Yabuta}, Acta Arith. 173, No. 3, 197--224 (2016; Zbl 1348.11045) Full Text: DOI arXiv
Kawaguchi, Shu; Silverman, Joseph H. Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties. (English) Zbl 1391.37078 Trans. Am. Math. Soc. 368, No. 7, 5009-5035 (2016); addendum ibid. 373, No. 3, 2253 (2020). MSC: 37P30 37P15 11G10 11G50 37P55 PDF BibTeX XML Cite \textit{S. Kawaguchi} and \textit{J. H. Silverman}, Trans. Am. Math. Soc. 368, No. 7, 5009--5035 (2016; Zbl 1391.37078) Full Text: DOI arXiv
Ingram, Patrick Variation of the canonical height for polynomials in several variables. (English) Zbl 1333.14024 Int. Math. Res. Not. 2015, No. 24, 13545-13562 (2015). Reviewer: Michel Waldschmidt (Paris) MSC: 14G40 14G25 37P05 PDF BibTeX XML Cite \textit{P. Ingram}, Int. Math. Res. Not. 2015, No. 24, 13545--13562 (2015; Zbl 1333.14024) Full Text: DOI arXiv
Pottmeyer, Lukas Heights of points with bounded ramification. (English) Zbl 1328.11074 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 14, No. 3, 965-981 (2015). Reviewer: David McKinnon (Waterloo) MSC: 11G50 37P30 14H52 PDF BibTeX XML Cite \textit{L. Pottmeyer}, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 14, No. 3, 965--981 (2015; Zbl 1328.11074) Full Text: DOI arXiv
Saha, Manideepa; Bandopadhyay, Sriparna Combinatorial properties of generalized \(M\)-matrices. (English) Zbl 1327.15069 Electron. J. Linear Algebra 30, 550-576 (2015). MSC: 15B48 15A21 05C50 PDF BibTeX XML Cite \textit{M. Saha} and \textit{S. Bandopadhyay}, Electron. J. Linear Algebra 30, 550--576 (2015; Zbl 1327.15069) Full Text: DOI
Bauchère, Hugues A lower bound for the canonical height of Drinfeld modules with complex multiplication. (Minoration de la hauteur canonique pour les modules de Drinfeld à multiplications complexes.) (French. English summary) Zbl 1327.11039 J. Number Theory 157, 291-328 (2015). Reviewer: Francesc Bars Cortina (Bellaterra) MSC: 11G09 11G50 11R37 PDF BibTeX XML Cite \textit{H. Bauchère}, J. Number Theory 157, 291--328 (2015; Zbl 1327.11039) Full Text: DOI arXiv
Lin, Qian; Wang, Ming-Xi Isogeny orbits in a family of abelian varieties. (English) Zbl 1382.11045 Acta Arith. 170, No. 2, 161-173 (2015). MSC: 11G18 11G50 14K10 PDF BibTeX XML Cite \textit{Q. Lin} and \textit{M.-X. Wang}, Acta Arith. 170, No. 2, 161--173 (2015; Zbl 1382.11045) Full Text: DOI arXiv
Hajli, Mounir Canonical heights of toric subvarieties. (Hauteurs canoniques des sous-variétés toriques.) (French) Zbl 1339.11070 J. Number Theory 153, 230-269 (2015). Reviewer: Ignacio García Marco (Lyon) MSC: 11G50 14G40 14M25 PDF BibTeX XML Cite \textit{M. Hajli}, J. Number Theory 153, 230--269 (2015; Zbl 1339.11070) Full Text: DOI arXiv
Fujita, Yasutsugu; Nara, Tadahisa Generators and integral points on twists of the Fermat cubic. (English) Zbl 1339.11066 Acta Arith. 168, No. 1, 1-16 (2015). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11G05 11D25 11G50 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{T. Nara}, Acta Arith. 168, No. 1, 1--16 (2015; Zbl 1339.11066) Full Text: DOI
Lee, Jung-Jo On the ranks of elliptic curves in families of quadratic twists over number fields. (English) Zbl 1349.11095 Czech. Math. J. 64, No. 4, 1003-1018 (2014). Reviewer: Andrea Bandini (Parma) MSC: 11G05 PDF BibTeX XML Cite \textit{J.-J. Lee}, Czech. Math. J. 64, No. 4, 1003--1018 (2014; Zbl 1349.11095) Full Text: DOI Link
Nara, Tadahisa Lower bounds of the canonical height on quadratic twists of elliptic curves. (English) Zbl 1322.11059 Rocky Mt. J. Math. 44, No. 6, 2009-2027 (2014). Reviewer: Andrej Dujella (Zagreb) MSC: 11G05 11G50 11G07 PDF BibTeX XML Cite \textit{T. Nara}, Rocky Mt. J. Math. 44, No. 6, 2009--2027 (2014; Zbl 1322.11059) Full Text: DOI arXiv Euclid
de Jong, Robin; Müller, J. Steffen Canonical heights and division polynomials. (English) Zbl 1306.11052 Math. Proc. Camb. Philos. Soc. 157, No. 2, 357-373 (2014). Reviewer: Michel Waldschmidt (Paris) MSC: 11G50 11J13 14H40 11G10 PDF BibTeX XML Cite \textit{R. de Jong} and \textit{J. S. Müller}, Math. Proc. Camb. Philos. Soc. 157, No. 2, 357--373 (2014; Zbl 1306.11052) Full Text: DOI arXiv
Silverman, Joseph H. Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space. (English) Zbl 1372.37093 Ergodic Theory Dyn. Syst. 34, No. 2, 647-678 (2014). MSC: 37F45 14E05 37B40 PDF BibTeX XML Cite \textit{J. H. Silverman}, Ergodic Theory Dyn. Syst. 34, No. 2, 647--678 (2014; Zbl 1372.37093) Full Text: DOI arXiv
Ingram, Patrick Canonical heights for Hénon maps. (English) Zbl 1323.37059 Proc. Lond. Math. Soc. (3) 108, No. 3, 780-808 (2014). Reviewer: Lingmin Liao (Créteil) MSC: 37P30 37P15 11G50 PDF BibTeX XML Cite \textit{P. Ingram}, Proc. Lond. Math. Soc. (3) 108, No. 3, 780--808 (2014; Zbl 1323.37059) Full Text: DOI arXiv
Nara, Tadahisa Mordell-Weil group of the twist family of elliptic curves and related topics. (Japanese. English summary) Zbl 1318.11077 RIMS Kôkyûroku Bessatsu B44, 141-149 (2013). MSC: 11G05 11G50 PDF BibTeX XML Cite \textit{T. Nara}, RIMS Kôkyûroku Bessatsu B44, 141--149 (2013; Zbl 1318.11077)
Lee, Chong Gyu The equidistribution of small points for strongly regular pairs of polynomial maps. (English) Zbl 1294.11114 Math. Z. 275, No. 3-4, 1047-1072 (2013). Reviewer: Yu Yasufuku (Tokyo) MSC: 11G50 14G50 32H50 37P05 37P30 PDF BibTeX XML Cite \textit{C. G. Lee}, Math. Z. 275, No. 3--4, 1047--1072 (2013; Zbl 1294.11114) Full Text: DOI arXiv
Ingram, Patrick Variation of the canonical height for a family of polynomials. (English) Zbl 1297.14028 J. Reine Angew. Math. 685, 73-97 (2013). Reviewer: Shun Tang (Beijing) MSC: 14G40 11G05 37P05 14J27 PDF BibTeX XML Cite \textit{P. Ingram}, J. Reine Angew. Math. 685, 73--97 (2013; Zbl 1297.14028) Full Text: DOI arXiv
Lin, Jan-Li; Wang, Chi-Hao Canonical height functions for monomial maps. (English) Zbl 1311.11056 Int. J. Number Theory 9, No. 7, 1821-1840 (2013). Reviewer: David McKinnon (Waterloo) MSC: 11G50 37P30 PDF BibTeX XML Cite \textit{J.-L. Lin} and \textit{C.-H. Wang}, Int. J. Number Theory 9, No. 7, 1821--1840 (2013; Zbl 1311.11056) Full Text: DOI arXiv
Kawaguchi, Shu Local and global canonical height functions for affine space regular automorphisms. (English) Zbl 1302.37067 Algebra Number Theory 7, No. 5, 1225-1252 (2013). MSC: 37P30 11G50 37P05 37P20 PDF BibTeX XML Cite \textit{S. Kawaguchi}, Algebra Number Theory 7, No. 5, 1225--1252 (2013; Zbl 1302.37067) Full Text: DOI arXiv
Kawaguchi, Shu Canonical vector heights on \(K3\) surfaces – a nonexistence result. (English) Zbl 1309.11055 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 24, No. 2, 181-197 (2013). Reviewer: David McKinnon (Waterloo) MSC: 11G50 37P30 PDF BibTeX XML Cite \textit{S. Kawaguchi}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 24, No. 2, 181--197 (2013; Zbl 1309.11055) Full Text: DOI
Voutier, Paul; Yabuta, Minoru Lang’s conjecture and sharp height estimates for the elliptic curves \(y^2 = x^3 + ax\). (English) Zbl 1304.11048 Int. J. Number Theory 9, No. 5, 1141-1170 (2013). Reviewer: Patrick Ingram (Fort Collins) MSC: 11G05 11G50 PDF BibTeX XML Cite \textit{P. Voutier} and \textit{M. Yabuta}, Int. J. Number Theory 9, No. 5, 1141--1170 (2013; Zbl 1304.11048) Full Text: DOI arXiv
Jonsson, Mattias; Wulcan, Elizabeth Canonical heights for plane polynomial maps of small topological degree. (English) Zbl 1302.37066 Math. Res. Lett. 19, No. 6, 1207-1217 (2012). MSC: 37P30 11G50 37P15 PDF BibTeX XML Cite \textit{M. Jonsson} and \textit{E. Wulcan}, Math. Res. Lett. 19, No. 6, 1207--1217 (2012; Zbl 1302.37066) Full Text: DOI arXiv Link
Silverman, Joseph H. Lehmer’s conjecture for polynomials satisfying a congruence divisibility condition and an analogue for elliptic curves. (English. French summary) Zbl 1264.11049 J. Théor. Nombres Bordx. 24, No. 3, 751-772 (2012). Reviewer: Artūras Dubickas (Vilnius) MSC: 11G05 11G50 11J97 PDF BibTeX XML Cite \textit{J. H. Silverman}, J. Théor. Nombres Bordx. 24, No. 3, 751--772 (2012; Zbl 1264.11049) Full Text: DOI Link
Akiyama, Shigeki; Drungilas, Paulius; Jankauskas, Jonas Height reducing problem on algebraic integers. (English) Zbl 1290.11144 Funct. Approximatio, Comment. Math. 47, No. 1, 105-119 (2012). MSC: 11R11 11R04 PDF BibTeX XML Cite \textit{S. Akiyama} et al., Funct. Approximatio, Comment. Math. 47, No. 1, 105--119 (2012; Zbl 1290.11144) Full Text: DOI Euclid
Holmes, David Computing Néron-Tate heights of points on hyperelliptic Jacobians. (English) Zbl 1239.14019 J. Number Theory 132, No. 6, 1295-1305 (2012). Reviewer: Enric Nart Viñals (Barcelona) MSC: 14G40 11G30 11G50 37P30 PDF BibTeX XML Cite \textit{D. Holmes}, J. Number Theory 132, No. 6, 1295--1305 (2012; Zbl 1239.14019) Full Text: DOI arXiv
Petsche, Clayton; Szpiro, Lucien; Tucker, Thomas J. A dynamical pairing between two rational maps. (English) Zbl 1300.37052 Trans. Am. Math. Soc. 364, No. 4, 1687-1710 (2012). MSC: 37P30 11G50 14G40 37P05 PDF BibTeX XML Cite \textit{C. Petsche} et al., Trans. Am. Math. Soc. 364, No. 4, 1687--1710 (2012; Zbl 1300.37052) Full Text: DOI arXiv
Fujita, Yasutsugu; Nara, Tadahisa On the Mordell-Weil group of the elliptic curve. (English) Zbl 1308.11059 J. Number Theory 132, No. 3, 448-466 (2012). MSC: 11G05 11G50 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{T. Nara}, J. Number Theory 132, No. 3, 448--466 (2012; Zbl 1308.11059) Full Text: DOI arXiv
Draziotis, Konstantinos A. On the number of integer points on the elliptic curve \(y^2 = x^3 + Ax\). (English) Zbl 1238.11037 Int. J. Number Theory 7, No. 3, 611-621 (2011). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D25 11G05 11D45 PDF BibTeX XML Cite \textit{K. A. Draziotis}, Int. J. Number Theory 7, No. 3, 611--621 (2011; Zbl 1238.11037) Full Text: DOI
Ih, Su-Ion A nondensity property of preperiodic points on Chebyshev dynamical systems. (English) Zbl 1214.11070 J. Number Theory 131, No. 4, 750-780 (2011). MSC: 37P15 11G05 11G35 11J71 14G05 37P30 37P35 PDF BibTeX XML Cite \textit{S.-I. Ih}, J. Number Theory 131, No. 4, 750--780 (2011; Zbl 1214.11070) Full Text: DOI
Jain, Sonal A new record for the canonical height on an elliptic curve over \(\mathbb C(t)\). (English) Zbl 1222.11087 New York J. Math. 16, 525-537 (2010). Reviewer: Fumio Hazama (Hatoyama) MSC: 11G50 14G40 11G05 PDF BibTeX XML Cite \textit{S. Jain}, New York J. Math. 16, 525--537 (2010; Zbl 1222.11087) Full Text: EuDML EMIS
Thongjunthug, Thotsaphon Computing a lower bound for the canonical height on elliptic curves over number fields. (English) Zbl 1231.11063 Math. Comput. 79, No. 272, 2431-2449 (2010). Reviewer: Carlos D’Andrea (Barcelona) MSC: 11G05 11Y16 11Y40 PDF BibTeX XML Cite \textit{T. Thongjunthug}, Math. Comput. 79, No. 272, 2431--2449 (2010; Zbl 1231.11063) Full Text: DOI
Fujita, Yasutsugu; Terai, Nobuhiro Generators for the elliptic curve \(y^2=x^3-nx\). (English) Zbl 1198.11053 Komatsu, Takao (ed.), Diophantine analysis and related fields 2010. DARF–2010. Proceedings of the conference, Musashino, Tokyo, Japan, March 4–5, 2010. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0815-9). AIP Conference Proceedings 1264, 1-6 (2010). Reviewer: Andreas Schweizer (Taipei) MSC: 11G05 11G50 14G05 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{N. Terai}, AIP Conf. Proc. 1264, 1--6 (2010; Zbl 1198.11053) Full Text: DOI
Silverman, Joseph H. Lang’s height conjecture and Szpiro’s conjecture. (English) Zbl 1304.11046 New York J. Math. 16, 1-12 (2010). Reviewer: Patrick Ingram (Fort Collins) MSC: 11G05 11G50 11J97 14H52 PDF BibTeX XML Cite \textit{J. H. Silverman}, New York J. Math. 16, 1--12 (2010; Zbl 1304.11046) Full Text: arXiv EMIS
Dąbrowski, Andrzej; Jȩdrzejak, Tomasz Ranks in families of Jacobian varieties of twisted Fermat curves. (English) Zbl 1216.11066 Can. Math. Bull. 53, No. 1, 58-63 (2010). Reviewer: Fumio Hazama (Hatoyama) MSC: 11G10 11G05 11G50 14G05 11G30 14H45 14K15 PDF BibTeX XML Cite \textit{A. Dąbrowski} and \textit{T. Jȩdrzejak}, Can. Math. Bull. 53, No. 1, 58--63 (2010; Zbl 1216.11066) Full Text: DOI
Jain, Sonal Minimal regulators for rank-2 subgroups of rational and \(K3\) elliptic surfaces. (English) Zbl 1222.14085 Exp. Math. 18, No. 4, 429-447 (2009). MSC: 14J27 14J28 11G50 PDF BibTeX XML Cite \textit{S. Jain}, Exp. Math. 18, No. 4, 429--447 (2009; Zbl 1222.14085) Full Text: DOI Euclid
Kawaguchi, Shu; Silverman, Joseph H. Canonical heights and the arithmetic complexity of morphisms on projective space. (English) Zbl 1221.11152 Pure Appl. Math. Q. 5, No. 4, 1201-1217 (2009). Reviewer: Michael Zieve (Ann Arbor) MSC: 11G50 14G40 37P30 PDF BibTeX XML Cite \textit{S. Kawaguchi} and \textit{J. H. Silverman}, Pure Appl. Math. Q. 5, No. 4, 1201--1217 (2009; Zbl 1221.11152) Full Text: DOI arXiv
Pineiro, Jorge Canonical metrics of commuting maps. (English) Zbl 1173.14306 Int. J. Mod. Math. 4, No. 1, 1-12 (2009). MSC: 14G40 14K22 14H52 16W22 28C10 PDF BibTeX XML Cite \textit{J. Pineiro}, Int. J. Mod. Math. 4, No. 1, 1--12 (2009; Zbl 1173.14306) Full Text: arXiv
Benedetto, Robert L.; Dickman, Benjamin; Joseph, Sasha; Krause, Benjamin; Rubin, Daniel; Zhou, Xinwen Computing points of small height for cubic polynomials. (English) Zbl 1194.37187 Involve 2, No. 1, 37-64 (2009). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 37P05 11C08 11G50 11S99 37P15 37P30 37P40 PDF BibTeX XML Cite \textit{R. L. Benedetto} et al., Involve 2, No. 1, 37--64 (2009; Zbl 1194.37187) Full Text: DOI arXiv
Yabuta, Minoru Elliptic divisibility sequences and certain Diophantine equations. (English) Zbl 1258.11064 Rocky Mt. J. Math. 39, No. 4, 1339-1352 (2009). Reviewer: Olaf Ninnemann (Berlin) MSC: 11G05 11B37 11B39 11D25 PDF BibTeX XML Cite \textit{M. Yabuta}, Rocky Mt. J. Math. 39, No. 4, 1339--1352 (2009; Zbl 1258.11064) Full Text: DOI
Ingram, Patrick Lower bounds on the canonical height associated to the morphism \(\phi(z)= z^d+c\). (English) Zbl 1239.11071 Monatsh. Math. 157, No. 1, 69-89 (2009). Reviewer: Thomas J. Tucker (Rochester) MSC: 11G50 37F10 11G99 PDF BibTeX XML Cite \textit{P. Ingram}, Monatsh. Math. 157, No. 1, 69--89 (2009; Zbl 1239.11071) Full Text: DOI arXiv
Baker, Matthew A finiteness theorem for canonical heights attached to rational maps over function fields. (English) Zbl 1187.37133 J. Reine Angew. Math. 626, 205-233 (2009). Reviewer: Paul Vojta (Berkeley) MSC: 37P05 37P15 37P30 14H52 14H05 14G40 PDF BibTeX XML Cite \textit{M. Baker}, J. Reine Angew. Math. 626, 205--233 (2009; Zbl 1187.37133) Full Text: DOI arXiv
Baker, Matthew; Ih, Su-ion; Rumely, Robert A finiteness property of torsion points. (English) Zbl 1182.11030 Algebra Number Theory 2, No. 2, 217-248 (2008). Reviewer: Florian Breuer (Stellenbosch) MSC: 11G50 37P30 11G05 11J71 11J86 PDF BibTeX XML Cite \textit{M. Baker} et al., Algebra Number Theory 2, No. 2, 217--248 (2008; Zbl 1182.11030) Full Text: DOI arXiv
Colares, A. Gervasio; De Lima, Henrique F. Space-like hypersurfaces with positive constant \(r\) -mean curvature in Lorentzian product spaces. (English) Zbl 1152.83323 Gen. Relativ. Gravitation 40, No. 10, 2131-2147 (2008). MSC: 83C05 83E05 PDF BibTeX XML Cite \textit{A. G. Colares} and \textit{H. F. De Lima}, Gen. Relativ. Gravitation 40, No. 10, 2131--2147 (2008; Zbl 1152.83323) Full Text: DOI
Everest, Graham; Ingram, Patrick; Mahé, Valéry; Stevens, Shaun The uniform primality conjecture for elliptic curves. (English) Zbl 1246.11117 Acta Arith. 134, No. 2, 157-181 (2008). MSC: 11G05 11A41 PDF BibTeX XML Cite \textit{G. Everest} et al., Acta Arith. 134, No. 2, 157--181 (2008; Zbl 1246.11117) Full Text: DOI arXiv
Thongjunthug, Thotsaphon Computing a lower bound for the canonical height on elliptic curves over totally real number fields. (English) Zbl 1230.11074 van der Poorten, Alfred J. (ed.) et al., Algorithmic number theory. 8th international symposium, ANTS-VIII Banff, Canada, May 17–22, 2008 Proceedings. Berlin: Springer (ISBN 978-3-540-79455-4/pbk). Lecture Notes in Computer Science 5011, 139-152 (2008). Reviewer: Carlos D’Andrea (Barcelona) MSC: 11G05 11Y16 11Y40 PDF BibTeX XML Cite \textit{T. Thongjunthug}, Lect. Notes Comput. Sci. 5011, 139--152 (2008; Zbl 1230.11074) Full Text: DOI
Kawaguchi, Shu Projective surface automorphisms of positive topological entropy from an arithmetic viewpoint. (English) Zbl 1144.14019 Am. J. Math. 130, No. 1, 159-186 (2008). Reviewer: Huayi Chen (Paris) MSC: 14G40 37C25 11G35 14J50 PDF BibTeX XML Cite \textit{S. Kawaguchi}, Am. J. Math. 130, No. 1, 159--186 (2008; Zbl 1144.14019) Full Text: DOI arXiv
Uchida, Yukihiro The difference between the ordinary height and the canonical height on elliptic curves. (English) Zbl 1145.11050 J. Number Theory 128, No. 2, 263-279 (2008). Reviewer: Lenny Fukshansky (Claremont) MSC: 11G50 11G05 11G07 14G05 PDF BibTeX XML Cite \textit{Y. Uchida}, J. Number Theory 128, No. 2, 263--279 (2008; Zbl 1145.11050) Full Text: DOI
Swinnerton-Dyer, Peter A canonical height on \(X^3_0=X_1 X_2 X_3\). (English) Zbl 1143.14018 Zannier, Umberto (ed.), Diophantine geometry. Selected papers of a the workshop, Pisa, Italy, April 12–July 22, 2005. Pisa: Edizioni della Normale (ISBN 978-88-7642-206-5/pbk). Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series (Nuova Serie) 4, 309-322 (2007). Reviewer: Roger Heath-Brown (Oxford) MSC: 14G05 11G50 14G10 14M25 PDF BibTeX XML Cite \textit{P. Swinnerton-Dyer}, CRM Ser. (N.S.) 4, 309--322 (2007; Zbl 1143.14018)
Kawaguchi, Shu Canonical heights for random iterations in certain varieties. (English) Zbl 1208.37056 Int. Math. Res. Not. 2007, No. 7, Article ID rnm023, 33 p. (2007). Reviewer: Paul Vojta (Berkeley) MSC: 37P30 11G50 14G40 PDF BibTeX XML Cite \textit{S. Kawaguchi}, Int. Math. Res. Not. 2007, No. 7, Article ID rnm023, 33 p. (2007; Zbl 1208.37056) Full Text: DOI arXiv
Kawaguchi, Shu; Silverman, Joseph H. Dynamics of projective morphisms having identical canonical heights. (English) Zbl 1130.11035 Proc. Lond. Math. Soc. (3) 95, No. 2, 519-544 (2007). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11G50 14G40 37F50 PDF BibTeX XML Cite \textit{S. Kawaguchi} and \textit{J. H. Silverman}, Proc. Lond. Math. Soc. (3) 95, No. 2, 519--544 (2007; Zbl 1130.11035) Full Text: DOI
Duquesne, Sylvain Elliptic curves associated with simplest quartic fields. (English) Zbl 1123.11018 J. Théor. Nombres Bordx. 19, No. 1, 81-100 (2007). Reviewer: Andreas Schweizer (Exeter) MSC: 11G05 11G50 PDF BibTeX XML Cite \textit{S. Duquesne}, J. Théor. Nombres Bordx. 19, No. 1, 81--100 (2007; Zbl 1123.11018) Full Text: DOI Numdam EuDML Link
Liţcanu, Răzvan Valuations, intersections and Belyi functions–some remarks on the construction of heights. (Valuations, intersections et fonctions de Belyi–quelques remarques sur la construction des hauteurs.) (French) Zbl 1142.14014 Expo. Math. 25, No. 2, 95-116 (2007). Reviewer: Paul Vojta (Berkeley) MSC: 14G40 14H25 14H30 PDF BibTeX XML Cite \textit{R. Liţcanu}, Expo. Math. 25, No. 2, 95--116 (2007; Zbl 1142.14014) Full Text: DOI
Szpiro, Lucien; Tucker, Thomas J. Algebraic dynamics. (English) Zbl 1231.11070 Zannier, Umberto (ed.), Colloquium De Giorgi 2006, Pisa, Italy. Pisa: Edizioni della Normale (ISBN 978-88-7642-212-6/pbk). Colloquia 1, 51-57 (2006). MSC: 11G50 14G40 37P30 PDF BibTeX XML Cite \textit{L. Szpiro} and \textit{T. J. Tucker}, Colloquia 1, 51--57 (2006; Zbl 1231.11070)
Kawaguchi, Shu Canonical height functions for affine plane automorphisms. (English) Zbl 1101.11019 Math. Ann. 335, No. 2, 285-310 (2006). Reviewer: Jan-Hendrik Evertse (Leiden) MSC: 11G50 32H50 14G40 37F10 PDF BibTeX XML Cite \textit{S. Kawaguchi}, Math. Ann. 335, No. 2, 285--310 (2006; Zbl 1101.11019) Full Text: DOI
Cremona, J. E.; Prickett, M.; Siksek, Samir Height difference bounds for elliptic curves over number fields. (English) Zbl 1162.11032 J. Number Theory 116, No. 1, 42-68 (2006). MSC: 11G50 11G05 11G07 14G05 PDF BibTeX XML Cite \textit{J. E. Cremona} et al., J. Number Theory 116, No. 1, 42--68 (2006; Zbl 1162.11032) Full Text: DOI
Ih, Su-ion Height uniformity for integral points on elliptic curves. (English) Zbl 1118.14026 Trans. Am. Math. Soc. 358, No. 4, 1657-1675 (2006). MSC: 11G50 14G05 11G05 11G35 PDF BibTeX XML Cite \textit{S.-i. Ih}, Trans. Am. Math. Soc. 358, No. 4, 1657--1675 (2006; Zbl 1118.14026) Full Text: DOI
Pineiro, Jorge; Szpiro, Lucien; Tucker, Thomas J. Mahler measure for dynamical systems on \(\mathbb P^1\) and intersection theory on a singular arithmetic surface. (English) Zbl 1101.11020 Bogomolov, Fedor (ed.) et al., Geometric methods in algebra and number theory. Basel: Birkhäuser (ISBN 0-8176-4349-4/hbk). Progress in Mathematics 235, 219-250 (2005). Reviewer: Paul Vojta (Berkeley) MSC: 11G50 14G40 37F10 PDF BibTeX XML Cite \textit{J. Pineiro} et al., Prog. Math. 235, 219--250 (2005; Zbl 1101.11020)
Baker, Matthew H.; Hsia, Liang-Chung Canonical heights, transfinite diameters, and polynomial dynamics. (English) Zbl 1071.11040 J. Reine Angew. Math. 585, 61-92 (2005). Reviewer: Thomas Ward (Norwich) MSC: 11G50 37B10 PDF BibTeX XML Cite \textit{M. H. Baker} and \textit{L.-C. Hsia}, J. Reine Angew. Math. 585, 61--92 (2005; Zbl 1071.11040) Full Text: DOI arXiv
Naumann, Niko Linear relations among the values of canonical heights from the existence of non-trivial endomorphisms. (English) Zbl 1087.11041 Can. Math. Bull. 47, No. 2, 271-279 (2004). Reviewer: Fumio Hazama (Hatoyama) MSC: 11G50 11G10 14K15 PDF BibTeX XML Cite \textit{N. Naumann}, Can. Math. Bull. 47, No. 2, 271--279 (2004; Zbl 1087.11041) Full Text: DOI arXiv
Carnochan Naqvi, Sarah; McDonald, Judith J. Eventually nonnegative matrices are similar to seminonnegative matrices. (English) Zbl 1052.15017 Linear Algebra Appl. 381, 245-258 (2004). Reviewer: Yueh-er Kuo (Knoxville) MSC: 15B48 15A21 PDF BibTeX XML Cite \textit{S. Carnochan Naqvi} and \textit{J. J. McDonald}, Linear Algebra Appl. 381, 245--258 (2004; Zbl 1052.15017) Full Text: DOI
Silverman, Joseph H. A lower bound for the canonical height on elliptic curves over abelian extensions. (English) Zbl 1053.11052 J. Number Theory 104, No. 2, 353-372 (2004). Reviewer: Horst G. Zimmer (Saarbrücken) MSC: 11G05 11G10 11G50 14G25 14K15 PDF BibTeX XML Cite \textit{J. H. Silverman}, J. Number Theory 104, No. 2, 353--372 (2004; Zbl 1053.11052) Full Text: DOI arXiv
Koblitz, Neal Good and bad uses of elliptic curves in cryptography. (English) Zbl 1063.11051 Mosc. Math. J. 2, No. 4, 693-715 (2002). MSC: 11T71 14G50 11G20 94A60 11Y16 94A62 PDF BibTeX XML Cite \textit{N. Koblitz}, Mosc. Math. J. 2, No. 4, 693--715 (2002; Zbl 1063.11051)
Stoll, Michael On the height constant for curves of genus two. II. (English) Zbl 1139.11318 Acta Arith. 104, No. 2, 165-182 (2002). MSC: 11G50 11G30 11G10 14G25 PDF BibTeX XML Cite \textit{M. Stoll}, Acta Arith. 104, No. 2, 165--182 (2002; Zbl 1139.11318) Full Text: DOI EuDML
Akiyama, Shigeki; Pethő, Attila On canonical number systems. (English) Zbl 0988.68101 Theor. Comput. Sci. 270, No. 1-2, 921-933 (2002). MSC: 11A63 11R09 68Q70 PDF BibTeX XML Cite \textit{S. Akiyama} and \textit{A. Pethő}, Theor. Comput. Sci. 270, No. 1--2, 921--933 (2002; Zbl 0988.68101) Full Text: DOI
Einsiedler, Manfred; Everest, Graham; Ward, Thomas B. Entropy and the canonical height. (English) Zbl 0994.11022 J. Number Theory 91, No. 2, 256-273 (2001). Reviewer: Jan-Hendrik Evertse (Leiden) MSC: 11G05 37A35 11G50 PDF BibTeX XML Cite \textit{M. Einsiedler} et al., J. Number Theory 91, No. 2, 256--273 (2001; Zbl 0994.11022) Full Text: DOI Link
Poonen, Bjorn Néron-Tate projection of algebraic points. (English) Zbl 1024.14008 Int. Math. Res. Not. 2001, No. 9, 435-440 (2001). MSC: 14G05 14K15 14G40 PDF BibTeX XML Cite \textit{B. Poonen}, Int. Math. Res. Not. 2001, No. 9, 435--440 (2001; Zbl 1024.14008) Full Text: DOI
Moriwaki, Atsushi The canonical arithmetic height of subvarieties of an abelian variety over a finitely generated field. (English) Zbl 1013.11032 J. Reine Angew. Math. 530, 33-54 (2001). MSC: 11G50 11G10 11G35 14G40 14K15 PDF BibTeX XML Cite \textit{A. Moriwaki}, J. Reine Angew. Math. 530, 33--54 (2001; Zbl 1013.11032) Full Text: DOI arXiv