Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Jaap Top"'
Autor:
Martin Djukanović, Jaap Top
Publikováno v:
Expositiones Mathematicae.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a5d7d5364b2e706c6af2cb13195da54b
https://doi.org/10.1016/j.exmath.2023.03.003
https://doi.org/10.1016/j.exmath.2023.03.003
Publikováno v:
Transactions of the american mathematical society, 375, 1653-1670. AMER MATHEMATICAL SOC
The problem of algebraic dependence of solutions to (non-linear) first order autonomous equations over an algebraically closed field of characteristic zero is given a `complete' answer, obtained independently of model theoretic results on differentia
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::96336babe5e9d1cefe3a1dfbfae455f8
https://research.rug.nl/en/publications/bcae018a-04a4-4362-965f-38e2c60cf9cb
https://research.rug.nl/en/publications/bcae018a-04a4-4362-965f-38e2c60cf9cb
Publikováno v:
Quaestiones Mathematicae; Vol. 45 No. 12 (2022); 1841-1853
Quaestiones mathematicae, 45(12), 1841-1853
Quaestiones mathematicae, 45(12), 1841-1853
This paper discusses prime numbers that are (resp. are not) congruent numbers. Particularly the only case not fully covered by earlier results, namely primes of the form $p=8k+1$, receives attention.
14 pages
14 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be040bd2452096f5c2aa9d38c34b6b8e
https://www.ajol.info/index.php/qm/article/view/239284
https://www.ajol.info/index.php/qm/article/view/239284
Publikováno v:
Indagationes Mathematicae, 32(4), 883-900. ELSEVIER SCIENCE BV
Indagationes Mathematicae. New Series, 32, 883-900
Indagationes Mathematicae. New Series, 32, 4, pp. 883-900
Indagationes Mathematicae. New Series, 32, 883-900
Indagationes Mathematicae. New Series, 32, 4, pp. 883-900
For the hyperelliptic curve C_p with equation y^2=x(x-2p)(x-p)(x+p)(x+2p) with p a prime number, we discuss bounds for the rank of its Jacobian over Q, find many cases having 2-torsion in the associated Shafarevich-Tate group, and we present some res
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e0928cafb4509e414821fd6d9c79d881
https://doi.org/10.1016/j.indag.2021.06.004
https://doi.org/10.1016/j.indag.2021.06.004
Autor:
Jaap Top
Publikováno v:
Contemporary Mathematics. :297-303
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::164b11be581e2f5264f4e1e771f2874b
https://doi.org/10.1090/conm/770/15441
https://doi.org/10.1090/conm/770/15441
Publikováno v:
Communications in algebra, 48(10), 4235-4248. Taylor & Francis Group
Given a polynomial $f$ with coefficients in a field of prime characteristic $p$, it is known that there exists a differential operator that raises $1/f$ to its $p$th power. We first discuss a relation between the `level' of this differential operator
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6146a90a46991fe8dba219178c0712ad
https://doi.org/10.1080/00927872.2020.1759614
https://doi.org/10.1080/00927872.2020.1759614
Publikováno v:
Research in Number Theory, 7(1):7. Springer Nature
This note reformulates Mazur’s result on the possible orders of rational torsion points on elliptic curves over$$\mathbb {Q}$$Qin a way that makes sense for arbitrary genus one curves, regardless whether or not the curve contains a rational point.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::09c2c6bb51712b2aa3fd3bc7d4f6fbbc
https://doi.org/10.1007/s40993-020-00231-z
https://doi.org/10.1007/s40993-020-00231-z
Autor:
Jaap Top, Eduardo Ruíz Duarte
Publikováno v:
Indian journal of pure & applied mathematics, 51(2), 761-776. INDIAN NAT SCI ACAD
We prove the Hasse-Weil inequality for genus 2 curves given by an equation of the form y^2 = f(x) with f a polynomial of degree 5, using arguments that mimic the elementary proof of the genus 1 case obtained by Yu. I. Manin in 1956.
Comment: Jou
Comment: Jou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4fffddbaafa3ccd991948c84617f1ce9
https://research.rug.nl/en/publications/d1502c50-4bee-48bb-be91-d5eeb9c38daa
https://research.rug.nl/en/publications/d1502c50-4bee-48bb-be91-d5eeb9c38daa
Autor:
Jaap Top, Carlo Verschoor
Publikováno v:
Journal de Théorie des Nombres de Bordeaux. 30:117-129
The Fricke-Macbeath curve is a smooth projective algebraic curve of genus 7 with automorphism group PSL₂(픽₈). We recall two models of it (introduced, respectively, by Maxim Hendriks and by Bradley Brock) defined over ℚ, and we establish an ex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8620750c6a99ac48a8cee0faea68b322
https://doi.org/10.5802/jtnb.1019
https://doi.org/10.5802/jtnb.1019
Publikováno v:
Symmetry, Integrability and Geometry, 15:088. NATL ACAD SCI UKRAINE, INST MATH
Symmetry, Integrability and Geometry: Methods and Applications
Vol. 15, (2019)
Acosta-Humánez P.B., Nonautonomous Hamiltonian systems and Morales-Ramis theory. I. The case x = f(x; t), SIAM J. Appl. Dyn. Syst. 8 (2009), 279{297, arXiv:0808.3028.
Acosta-Humánez P.B., van der Put M., Top J., Isomonodromy for the degenerate fth Painlevé equation, SIGMA 13 (2017), 029, 14 pages, arXiv:1612.03674.
Casale G.,Weil J.A., Galoisian methods for testing irreducibility of order two nonlinear differential equations, Paci c J. Math. 297 (2018), 299{337, arXiv:1504.08134.
Clarkson P.A., Painlevé equations-nonlinear special functions, slides presented during the IMA Summer Program Special Functions in the Digital Age, Minneapolis, July 22-August 2, 2002, available at http: //www.math.rug.nl/~top/Clarkson.pdf.
Clarkson P.A., Special polynomials associated with rational solutions of the fth Painlevé equation, J. Com-put. Appl. Math. 178 (2005), 111{129.
Clarkson P.A., Painlevé equations-nonlinear special functions, in Orthogonal Polynomials and Special Functions, Lecture Notes in Math., Vol. 1883, Editors F. Marcellán, W. Van Assche, Springer, Berlin, 2006, 331{411.
Gromak V.I., Laine I., Shimomura S., Painlevé differential equations in the complex plane, De Gruyter Studies in Mathematics, Vol. 28, Walter de Gruyter & Co., Berlin, 2002.
Horozov E., Stoyanova T., Non-integrability of some Painlevé VI-equations and dilogarithms, Regul. Chaotic Dyn. 12 (2007), 622{629.
Jimbo M., Miwa T., Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II, Phys. D 2 (1981), 407{448.
Lukashevich N.A., On the theory of Painlevé's third equation, Differ. Uravn. 3 (1967), 1913{1923.
Lukashevich N.A., The solutions of Painlevé's fth equation, Differ. Uravn. 4 (1968), 1413{1420.
Matsuda M., First-order algebraic differential equations. A differential algebraic approach, Lecture Notes in Math., Vol. 804, Springer, Berlin, 1980.
Morales-Ruiz J.J., A remark about the Painlevé transcendents, in Théories asymptotiques et équations de Painlevé, Sémin. Congr., Vol. 14, Soc. Math. France, Paris, 2006, 229-235.
Morales-Ruiz J.J., Ramis J.P., Galoisian obstructions to integrability of Hamiltonian systems, Methods Appl. Anal. 8 (2001), 33{96.
Morales-Ruiz J.J., Ramis J.P., Simo C., Integrability of Hamiltonian systems and differential Galois groups of higher variational equations, Ann. Sci. École Norm. Sup. (4) 40 (2007), 845-884.
Muntingh G., van der Put M., Order one equations with the Painlevé property, Indag. Math. (N.S.) 18 (2007), 83-95, arXiv:1202.4633.
Nagloo J., Pillay A., On algebraic relations between solutions of a generic Painlevé equation, J. Reine Angew. Math. 726 (2017), 1{27, arXiv:1112.2916.
Ngo Chau L.X., Nguyen K.A., van der Put M., Top J., Equivalence of differential equations of order one, J. Symbolic Comput. 71 (2015), 47{59, arXiv:1303.4960.
Ohyama Y., Kawamuko H., Sakai H., Okamoto K., Studies on the Painlevé equations. V. Third Painlevé equations of special type PIII(D7) and PIII(D8), J. Math. Sci. Univ. Tokyo 13 (2006), 145{204.
Ohyama Y., Okumura S., R. Fuchs' problem of the Painlevé equations from the rst to the fth, in Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, Contemp. Math., Vol. 593, Amer. Math. Soc., Providence, RI, 2013, 163{178, arXiv:math.CA/0512243.
Stoyanova T., Non-integrability of Painlevé VI equations in the Liouville sense, Nonlinearity 22 (2009), 2201{2230.
Stoyanova T., Non-integrability of Painlevé V equations in the Liouville sense and Stokes phenomenon, Adv. Pure Math. 1 (2011), 170{183.
Stoyanova T., A note on the R. Fuchs's problem for the Painlevé equations, arXiv:1204.0157.
Stoyanova T., Non-integrability of the fourth Painlevé equation in the Liouville-Arnold sense, Nonlinearity 27 (2014), 1029-1044.
Stoyanova T., Christov O., Non-integrability of the second Painlevé equation as a Hamiltonian system, C. R. Acad. Bulgare Sci. 60 (2007), 13{18, arXiv:1103.2443.
Umemura H., On the irreducibility of the rst differential equation of Painlevé, in Algebraic Geometry and Commutative Algebra, Vol. II, Kinokuniya, Tokyo, 1988, 771-789.
Umemura H., Second proof of the irreducibility of the rst differential equation of Painlevé, Nagoya Math. J. 117 (1990), 125{171.
Umemura H., Birational automorphism groups and differential equations, Nagoya Math. J. 119 (1990), 1{80.
Umemura H., Watanabe H., Solutions of the second and fourth Painlevé equations. I, Nagoya Math. J. 148 (1997), 151{198.
van der Put M., Saito M.H., Moduli spaces for linear differential equations and the Painlevé equations, Ann. Inst. Fourier (Grenoble) 59 (2009), 2611{2667, arXiv:0902.1702.
van der Put M., Singer M.F., Galois theory of linear differential equations, Grundlehren der Mathematischen Wissenschaften, Vol. 328, Springer-Verlag, Berlin, 2003.
Z_ ol ádek H., Filipuk G., Painlevé equations, elliptic integrals and elementary functions, J. Differential Equa-tions 258 (2015), 1303{1355.
Symmetry, Integrability and Geometry: Methods and Applications
Vol. 15, (2019)
Acosta-Humánez P.B., Nonautonomous Hamiltonian systems and Morales-Ramis theory. I. The case x = f(x; t), SIAM J. Appl. Dyn. Syst. 8 (2009), 279{297, arXiv:0808.3028.
Acosta-Humánez P.B., van der Put M., Top J., Isomonodromy for the degenerate fth Painlevé equation, SIGMA 13 (2017), 029, 14 pages, arXiv:1612.03674.
Casale G.,Weil J.A., Galoisian methods for testing irreducibility of order two nonlinear differential equations, Paci c J. Math. 297 (2018), 299{337, arXiv:1504.08134.
Clarkson P.A., Painlevé equations-nonlinear special functions, slides presented during the IMA Summer Program Special Functions in the Digital Age, Minneapolis, July 22-August 2, 2002, available at http: //www.math.rug.nl/~top/Clarkson.pdf.
Clarkson P.A., Special polynomials associated with rational solutions of the fth Painlevé equation, J. Com-put. Appl. Math. 178 (2005), 111{129.
Clarkson P.A., Painlevé equations-nonlinear special functions, in Orthogonal Polynomials and Special Functions, Lecture Notes in Math., Vol. 1883, Editors F. Marcellán, W. Van Assche, Springer, Berlin, 2006, 331{411.
Gromak V.I., Laine I., Shimomura S., Painlevé differential equations in the complex plane, De Gruyter Studies in Mathematics, Vol. 28, Walter de Gruyter & Co., Berlin, 2002.
Horozov E., Stoyanova T., Non-integrability of some Painlevé VI-equations and dilogarithms, Regul. Chaotic Dyn. 12 (2007), 622{629.
Jimbo M., Miwa T., Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II, Phys. D 2 (1981), 407{448.
Lukashevich N.A., On the theory of Painlevé's third equation, Differ. Uravn. 3 (1967), 1913{1923.
Lukashevich N.A., The solutions of Painlevé's fth equation, Differ. Uravn. 4 (1968), 1413{1420.
Matsuda M., First-order algebraic differential equations. A differential algebraic approach, Lecture Notes in Math., Vol. 804, Springer, Berlin, 1980.
Morales-Ruiz J.J., A remark about the Painlevé transcendents, in Théories asymptotiques et équations de Painlevé, Sémin. Congr., Vol. 14, Soc. Math. France, Paris, 2006, 229-235.
Morales-Ruiz J.J., Ramis J.P., Galoisian obstructions to integrability of Hamiltonian systems, Methods Appl. Anal. 8 (2001), 33{96.
Morales-Ruiz J.J., Ramis J.P., Simo C., Integrability of Hamiltonian systems and differential Galois groups of higher variational equations, Ann. Sci. École Norm. Sup. (4) 40 (2007), 845-884.
Muntingh G., van der Put M., Order one equations with the Painlevé property, Indag. Math. (N.S.) 18 (2007), 83-95, arXiv:1202.4633.
Nagloo J., Pillay A., On algebraic relations between solutions of a generic Painlevé equation, J. Reine Angew. Math. 726 (2017), 1{27, arXiv:1112.2916.
Ngo Chau L.X., Nguyen K.A., van der Put M., Top J., Equivalence of differential equations of order one, J. Symbolic Comput. 71 (2015), 47{59, arXiv:1303.4960.
Ohyama Y., Kawamuko H., Sakai H., Okamoto K., Studies on the Painlevé equations. V. Third Painlevé equations of special type PIII(D7) and PIII(D8), J. Math. Sci. Univ. Tokyo 13 (2006), 145{204.
Ohyama Y., Okumura S., R. Fuchs' problem of the Painlevé equations from the rst to the fth, in Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, Contemp. Math., Vol. 593, Amer. Math. Soc., Providence, RI, 2013, 163{178, arXiv:math.CA/0512243.
Stoyanova T., Non-integrability of Painlevé VI equations in the Liouville sense, Nonlinearity 22 (2009), 2201{2230.
Stoyanova T., Non-integrability of Painlevé V equations in the Liouville sense and Stokes phenomenon, Adv. Pure Math. 1 (2011), 170{183.
Stoyanova T., A note on the R. Fuchs's problem for the Painlevé equations, arXiv:1204.0157.
Stoyanova T., Non-integrability of the fourth Painlevé equation in the Liouville-Arnold sense, Nonlinearity 27 (2014), 1029-1044.
Stoyanova T., Christov O., Non-integrability of the second Painlevé equation as a Hamiltonian system, C. R. Acad. Bulgare Sci. 60 (2007), 13{18, arXiv:1103.2443.
Umemura H., On the irreducibility of the rst differential equation of Painlevé, in Algebraic Geometry and Commutative Algebra, Vol. II, Kinokuniya, Tokyo, 1988, 771-789.
Umemura H., Second proof of the irreducibility of the rst differential equation of Painlevé, Nagoya Math. J. 117 (1990), 125{171.
Umemura H., Birational automorphism groups and differential equations, Nagoya Math. J. 119 (1990), 1{80.
Umemura H., Watanabe H., Solutions of the second and fourth Painlevé equations. I, Nagoya Math. J. 148 (1997), 151{198.
van der Put M., Saito M.H., Moduli spaces for linear differential equations and the Painlevé equations, Ann. Inst. Fourier (Grenoble) 59 (2009), 2611{2667, arXiv:0902.1702.
van der Put M., Singer M.F., Galois theory of linear differential equations, Grundlehren der Mathematischen Wissenschaften, Vol. 328, Springer-Verlag, Berlin, 2003.
Z_ ol ádek H., Filipuk G., Painlevé equations, elliptic integrals and elementary functions, J. Differential Equa-tions 258 (2015), 1303{1355.
This paper first discusses irreducibility of a Painlev\'e equation $P$. We explain how the Painlev\'e property is helpful for the computation of special classical and algebraic solutions. As in a paper of Morales-Ruiz we associate an autonomous Hamil
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d97ef2df4f95eae41c08714581034df3
https://doi.org/10.3842/SIGMA.2019.088
https://doi.org/10.3842/SIGMA.2019.088