메뉴 건너뛰기




Volumn 99, Issue 3, 2001, Pages 227-256

Genus one curves defined by separated variable polynomials and a polynomial Pell equation

Author keywords

Chebyshev and Dickson polynomials; Computer based calculations; Genus one curves; Modular curves; Polynomial pell equations; Separated variable polynomials

Indexed keywords


EID: 0035657445     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa99-3-2     Document Type: Article
Times cited : (30)

References (34)
  • 2
    • 0007370241 scopus 로고    scopus 로고
    • A study on polynomials in separated variables with low genus factors
    • Dissertation, (Mathematik und Informatik), University of Essen
    • R. M. Avanzi, A study on polynomials in separated variables with low genus factors, Dissertation, Fachbereich 6 (Mathematik und Informatik), University of Essen, 2001.
    • (2001) Fachbereich , vol.6
    • Avanzi, R.M.1
  • 3
    • 0002344692 scopus 로고    scopus 로고
    • Irreducibility of polynomials and arithmetic progressions with equal product of terms
    • F. Beukers, T. N. Shorey and R. Tijdeman, Irreducibility of polynomials and arithmetic progressions with equal product of terms, in [GIU], 11-26.
    • GIU , pp. 11-26
    • Beukers, F.1    Shorey, T.N.2    Tijdeman, R.3
  • 4
    • 0040106485 scopus 로고    scopus 로고
    • Quadratic factors of f(x) - g(y)
    • Yu. F. Bilu, Quadratic factors of f(x) - g(y), Acta Arith. 90 (1999), 341-355.
    • (1999) Acta Arith. , vol.90 , pp. 341-355
    • Bilu, Yu.F.1
  • 5
    • 0039601022 scopus 로고    scopus 로고
    • The diophantine equation f(x) - g(y)
    • Yu. F. Bilu and R. F. Tichy, The Diophantine equation f(x) - g(y), ibid. 95 (2000), 261-288.
    • (2000) Acta Arith. , vol.95 , pp. 261-288
    • Bilu, Yu.F.1    Tichy, R.F.2
  • 6
    • 0032355643 scopus 로고    scopus 로고
    • Factorisations explicites de g(y) - h(z)
    • P. Cassou-Noguès et J.-M. Couveignes, Factorisations explicites de g(y) - h(z), ibid. 87 (1999), 291-317.
    • (1999) Acta Arith. , vol.87 , pp. 291-317
    • Cassou-Noguès, P.1    Couveignes, J.-M.2
  • 10
    • 0009446762 scopus 로고
    • A criterion of absolute irreducibility of polynomials
    • in Polish
    • A. Ehrenfeucht, A criterion of absolute irreducibility of polynomials, Prace Mat. 2 (1958), 167-169 (in Polish).
    • (1958) Prace Mat. , vol.2 , pp. 167-169
    • Ehrenfeucht, A.1
  • 11
    • 34250151276 scopus 로고
    • Endlichkeitssätze für abelsche varietäten über zahlkörpern
    • Erratum, ibid. 75 (1984), 381
    • G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349-366. Erratum, ibid. 75 (1984), 381.
    • (1983) Invent. Math. , vol.73 , pp. 349-366
    • Faltings, G.1
  • 12
    • 84961479443 scopus 로고
    • On a theorem of Ritt and related diophantine problems
    • M. Fried, On a theorem of Ritt and related diophantine problems, J. Reine Angew. Math. 264 (1973), 40-55.
    • (1973) J. Reine Angew. Math. , vol.264 , pp. 40-55
    • Fried, M.1
  • 13
    • 84972541889 scopus 로고
    • The field of definition of function fields and a problem in the reducibility of polynomials in two variables
    • _, The field of definition of function fields and a problem in the reducibility of polynomials in two variables, Illinois J. Math. 17 (1973), 128-146.
    • (1973) Illinois J. Math. , vol.17 , pp. 128-146
  • 14
    • 0000715930 scopus 로고
    • Exposition on an arithmetic-group theoretic connection via Riemann's existence theorem
    • Amer. Math. Soc.
    • _, Exposition on an arithmetic-group theoretic connection via Riemann's existence theorem, in: Proc. Sympos. Pure Math. 37, Amer. Math. Soc., 1980, 571-601.
    • (1980) Proc. Sympos. Pure Math. , vol.37 , pp. 571-601
  • 15
    • 0345277696 scopus 로고    scopus 로고
    • Variables separated polynomials, the genus 0 problem and moduli spaces
    • _, Variables separated polynomials, the genus 0 problem and moduli spaces, in [GIU], 169-228.
    • GIU , pp. 169-228
  • 17
    • 0007370243 scopus 로고
    • Equation de pell et points d'ordre fini
    • Appendix 93-95
    • Y. Hellegouarch et M. Lozach, Equation de Pell et points d'ordre fini, Publ. Math. Orsay 86/01 (1986), 72-92; Appendix 93-95.
    • (1986) Publ. Math. Orsay , vol.86 , Issue.1 , pp. 72-92
    • Hellegouarch, Y.1    Lozach, M.2
  • 19
    • 0003063953 scopus 로고
    • Old and new conjectured diophantine inequalities
    • S. Lang, Old and new conjectured diophantine inequalities, Bull. Amer. Math. Soc. (N.S.) 23 (1990), 37-75.
    • (1990) Bull. Amer. Math. Soc. (N.S.) , vol.23 , pp. 37-75
    • Lang, S.1
  • 21
  • 22
    • 0001658780 scopus 로고
    • Rational isogenies of prime degree
    • _, Rational isogenies of prime degree, Invent. Math. 44 (1978), 129-162.
    • (1978) Invent. Math. , vol.44 , pp. 129-162
  • 23
    • 0011153744 scopus 로고    scopus 로고
    • Bornes pour la torsion des courbes elliptiques sur les corps de nombres
    • L. Merel, Bornes pour la torsion des courbes elliptiques sur les corps de nombres, ibid. 124 (1996), 437-449.
    • (1996) Invent. Math. , vol.124 , pp. 437-449
    • Merel, L.1
  • 24
    • 0000039162 scopus 로고
    • Primitive monodromy groups of polynomials
    • Recent Developments in the Inverse Galois Problem, M. Fried (ed.), Amer. Math. Soc.
    • P. F. Müller, Primitive monodromy groups of polynomials, in: Recent Developments in the Inverse Galois Problem, M. Fried (ed.), Contemp. Math. 186, Amer. Math. Soc., 1995, 385-401.
    • (1995) Contemp. Math. , vol.186 , pp. 385-401
    • Müller, P.F.1
  • 26
    • 0033481392 scopus 로고    scopus 로고
    • Bornes effectives pour la torsion des courbes elliptiques sur le corps de nombres
    • P. Parent, Bornes effectives pour la torsion des courbes elliptiques sur le corps de nombres, J. Reine Angew. Math. 506 (1999), 85-116.
    • (1999) J. Reine Angew. Math. , vol.506 , pp. 85-116
    • Parent, P.1
  • 27
    • 0002533613 scopus 로고
    • Prime and composite polynomials
    • J. F. Ritt, Prime and composite polynomials, Trans. Amer. Math. Soc. 23 (1922), 51-66.
    • (1922) Trans. Amer. Math. Soc. , vol.23 , pp. 51-66
    • Ritt, J.F.1
  • 28
    • 0001638307 scopus 로고
    • On some problems of the arithmetical theory of continued fractions
    • A. Schinzel, On some problems of the arithmetical theory of continued fractions, Acta Arith. 6 (1961), 393-413.
    • (1961) Acta Arith. , vol.6 , pp. 393-413
    • Schinzel, A.1
  • 29
    • 0000115809 scopus 로고
    • On some problems of the arithmetical theory of continued fractions II
    • Corrigendum, ibid. 47 (1986), 295
    • _, On some problems of the arithmetical theory of continued fractions II, ibid. 7 (1962), 287-298. Corrigendum, ibid. 47 (1986), 295.
    • (1962) Acta Arith. , vol.7 , pp. 287-298
  • 31
    • 0001764679 scopus 로고
    • Über einige anwendungen diophantischer approximation
    • C. L. Siegel, Über einige Anwendungen diophantischer Approximation, Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1 (1929), 41-69.
    • (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. , vol.1 , pp. 41-69
    • Siegel, C.L.1
  • 33
    • 0007372970 scopus 로고
    • A remark on Ehrenfeucht's criterion for the irreducibility of polynomials
    • H. Tverberg, A remark on Ehrenfeucht's criterion for the irreducibility of polynomials, Prace Mat. 8 (1963/64), 117-118.
    • (1963) Prace Mat. , vol.8 , pp. 117-118
    • Tverberg, H.1
  • 34
    • 0007456744 scopus 로고
    • Ritt's second theorem in arbitrary characteristic
    • U. Zannier, Ritt's Second Theorem in arbitrary characteristic, J. Reine Angew. Math. 445 (1993), 175-203.
    • (1993) J. Reine Angew. Math. , vol.445 , pp. 175-203
    • Zannier, U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.