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Volumn 140, Issue 4, 2004, Pages 952-992

One- and two-level densities for rational families of elliptic curves: Evidence for the underlying group symmetries

Author keywords

Birch and Swinnerton Dyer conjecture; Elliptic curve L functions; Low lying zeros; N level density

Indexed keywords


EID: 16244399467     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0010437X04000582     Document Type: Article
Times cited : (99)

References (37)
  • 2
    • 0000857321 scopus 로고
    • The parity of the rank of the Mordcll-Weil group
    • B. Birch and N. Stephens. The parity of the rank of the Mordcll-Weil group, Topology 5 (1966). 295-299.
    • (1966) Topology , vol.5 , pp. 295-299
    • Birch, B.1    Stephens, N.2
  • 5
    • 0039302012 scopus 로고    scopus 로고
    • On the modularity of elliptic curves over Q: Wild 3-adic exercises
    • C. Breuil, B. Conrad, F. Diamond and R. Taylor, On the modularity of elliptic curves over Q: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), 843-939.
    • (2001) J. Amer. Math. Soc , vol.14 , pp. 843-939
    • Breuil, C.1    Conrad, B.2    Diamond, F.3    Taylor, R.4
  • 6
    • 0001081335 scopus 로고
    • The average rank of elliptic curves I
    • A. Brumer, The average rank of elliptic curves I, Invent. Math. 109 (1992). 445-472.
    • (1992) Invent. Math , vol.109 , pp. 445-472
    • Brumer, A.1
  • 7
    • 43449094744 scopus 로고    scopus 로고
    • The average rank of elliptic curves V
    • Preprint
    • A. Brumer and R. Heath-Brown, The average rank of elliptic curves V, Preprint.
    • Brumer, A.1    Heath-Brown, R.2
  • 10
    • 0003231477 scopus 로고
    • Multiplicative number theory
    • second edition, Springer, New York, revised by H. Montgomery
    • H. Davenport, Multiplicative number theory, second edition, Graduate Texts in Mathematics, vol. 74 (Springer, New York, 1980), revised by H. Montgomery.
    • (1980) Graduate Texts in Mathematics , vol.74
    • Davenport, H.1
  • 12
    • 84963009292 scopus 로고
    • On the triple correlation of zeros of the zeta function
    • D. Hejhal, On the triple correlation of zeros of the zeta function, Internat. Math. Res. Notices (1994), 294-302.
    • (1994) Internat. Math. Res. Notices , pp. 294-302
    • Hejhal, D.1
  • 13
    • 1842779976 scopus 로고    scopus 로고
    • ABC allows us to count squarefrees
    • Granville, ABC allows us to count squarefrees, Internat. Math. Res. Notices 19 (1998), 991-1009.
    • (1998) Internat. Math. Res. Notices , vol.19 , pp. 991-1009
    • Granville1
  • 15
    • 33646369881 scopus 로고    scopus 로고
    • On the distribution of root numbers in families of elliptic curves
    • Preprint
    • H. Helfgott, On the distribution of root numbers in families of elliptic curves, Preprint.
    • Helfgott, H.1
  • 18
    • 0003253039 scopus 로고    scopus 로고
    • Random matrices, Frobenius eigenvalues and monodromy
    • American Mathematical Society, Providence, RI
    • N. Katz and P. Sarnak, Random matrices, Frobenius eigenvalues and monodromy, Amer. Math. Soc. Colloq. Publ., vol. 45 (American Mathematical Society, Providence, RI, 1999).
    • (1999) Amer. Math. Soc. Colloq. Publ , vol.45
    • Katz, N.1    Sarnak, P.2
  • 19
    • 0033485102 scopus 로고    scopus 로고
    • Zeros of zeta functions and symmetries
    • N. Katz and P. Sarnak, Zeros of zeta functions and symmetries, Bull. Amer. Math. Soc. 36 (1999), 1-26.
    • (1999) Bull. Amer. Math. Soc , vol.36 , pp. 1-26
    • Katz, N.1    Sarnak, P.2
  • 20
    • 0004263205 scopus 로고
    • Princeton University Press, Princeton
    • A. Knapp, Elliptic curves (Princeton University Press, Princeton, 1992).
    • (1992) Elliptic curves
    • Knapp, A.1
  • 21
    • 0001543668 scopus 로고
    • Formules explicites el minorations de conducteurs de variétés algébriques
    • J. Mestre, Formules explicites el minorations de conducteurs de variétés algébriques, Compositio Math. 58 (1986), 209-232.
    • (1986) Compositio Math , vol.58 , pp. 209-232
    • Mestre, J.1
  • 22
    • 0000155470 scopus 로고
    • Rang moyen de families de courbes elliptiques et lois de Sato - Tate
    • P. Michel, Rang moyen de families de courbes elliptiques et lois de Sato - Tate, Monatsh. Math. 120 (1995), 127-136.
    • (1995) Monatsh. Math , vol.120 , pp. 127-136
    • Michel, P.1
  • 24
    • 0000308274 scopus 로고
    • The pair correlation of zeros of the zeta function
    • American Mathematical Society, Providence, RI
    • H. Montgomery, The pair correlation of zeros of the zeta function, in Analytic number theory, Proc. Symp. Pure Math., vol. 24 (American Mathematical Society, Providence, RI, 1973), 181-193.
    • (1973) Analytic number theory, Proc. Symp. Pure Math , vol.24 , pp. 181-193
    • Montgomery, H.1
  • 25
    • 0030646965 scopus 로고    scopus 로고
    • (t)-rank of elliptic curves and certain limit coming from the local points
    • K. Nagao, ℚ(t)-rank of elliptic curves and certain limit coming from the local points, Manuscripta Math. 92 (1997), 13-32.
    • (1997) Manuscripta Math , vol.92 , pp. 13-32
    • Nagao, K.1
  • 27
    • 43449111267 scopus 로고    scopus 로고
    • Average root numbers for a non-constant family of elliptic curves
    • Preprint
    • O. Rizzo, Average root numbers for a non-constant family of elliptic curves, Preprint.
    • Rizzo, O.1
  • 28
    • 0032371702 scopus 로고    scopus 로고
    • On the rank of an elliptic surface
    • M. Rosen and J. Silverman, On the rank of an elliptic surface, Invent. Math. 133 (1998), 43-67.
    • (1998) Invent. Math , vol.133 , pp. 43-67
    • Rosen, M.1    Silverman, J.2
  • 30
    • 0000580673 scopus 로고    scopus 로고
    • Zeros of principal L-functions and random matrix theory
    • Z. Rudnick and P. Sarnak, Zeros of principal L-functions and random matrix theory, Duke Math. J. 81 (1996), 269-322.
    • (1996) Duke Math. J , vol.81 , pp. 269-322
    • Rudnick, Z.1    Sarnak, P.2
  • 31
    • 0003357475 scopus 로고
    • The arithmetic of elliptic curves
    • Springer, Berlin
    • J. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106 (Springer, Berlin, 1986).
    • (1986) Graduate Texts in Mathematics , vol.106
    • Silverman, J.1
  • 32
    • 0003236499 scopus 로고
    • Advanced topics in the arithmetic of elliptic curves
    • Springer, Berlin
    • J. Silverman, Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 151 (Springer, Berlin, 1994).
    • (1994) Graduate Texts in Mathematics , vol.151
    • Silverman, J.1
  • 33
    • 0032221909 scopus 로고    scopus 로고
    • The average rank of an algebraic family of elliptic curves
    • J. Silverman, The average rank of an algebraic family of elliptic curves, J. reine angew. Math. 504 (1998), 227-236.
    • (1998) J. reine angew. Math , vol.504 , pp. 227-236
    • Silverman, J.1
  • 34
    • 0002526955 scopus 로고
    • Algebraic cycles and poles of zeta functions
    • Harper and Row, New York
    • J. T. Tate, Algebraic cycles and poles of zeta functions, in Arithmetical Algebraic Geometry (Harper and Row, New York, 1965), 93-110.
    • (1965) Arithmetical Algebraic Geometry , pp. 93-110
    • Tate, J.T.1
  • 35
    • 0000674810 scopus 로고
    • Ring-theoretic properties of certain Hecke algebras
    • R. Taylor and A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), 553-572.
    • (1995) Ann. of Math. (2) , vol.141 , pp. 553-572
    • Taylor, R.1    Wiles, A.2
  • 36
    • 84968484487 scopus 로고
    • Class numbers of the simplest cubic fields
    • L. Washington, Class numbers of the simplest cubic fields, Math. Comp. 48 (1987), 371-384.
    • (1987) Math. Comp , vol.48 , pp. 371-384
    • Washington, L.1
  • 37
    • 0000603921 scopus 로고
    • Modular elliptic curves and Fermat's last theorem
    • A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995), 443-551.
    • (1995) Ann. of Math. (2) , vol.141 , pp. 443-551
    • Wiles, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.