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Abstrakty
We study the family of curves Fm(p) : xp + yp = m, where p is an odd prime and m is a pth power free integer. We prove some results about the distribution of root numbers of the L-functions of the hyperelliptic curves associated to the curves Fm(p). As a corollary we conclude that the Jacobians of the curves Fm(5) with even analytic rank and those with odd analytic rank are equally distributed.
Wydawca
Rocznik
Tom
Strony
199--206
Opis fizyczny
Bibliogr. 8 poz.
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autor
- Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland, tjedrzejak@gmail.com
Bibliografia
- [1] A. Dąbrowski and T. Jędrzejak, Ranks in families of Jacobian varieties of twisted Fermat curves, Canad. Math. Bull., to appear.
- [2] A. Dąbrowski and J. Pomykała, Nonvanishing of motivic L-functions, Math. Proc. Cambridge Philos. Soc. 130 (2001), 221-235.
- [3] D. K. Faddeev, The group of divisor classes on some algebraic curves, Soviet Math. Dokl. 2 (1961), 67-69.
- [4] —, Invariants of divisor classes for the curves xk(l — x) = yl in the l-adic cyclotomic field, Trudy Mat. Inst. Steklov. 64 (1961), 284-293 (in Russian).
- [5] H. Iwaniec and P. Sarnak, The non-vanishing of central values of automorphic L-functions and Landau-Siegel zeros, Israel J. Math. 120 (2000), 155-177.
- [6] L. Mai, The analytic rank of a family of elliptic curves, Canad. J. Math. 45 (1993), 847-862.
- [7] W. Narkiewicz, Number Theory, Biblioteka Mat. 50, PWN, Warszawa, 1977 (in Polish); English transl.: World Sci., 1983.
- [8] M. Stoll, On the arithmetic of the curves y2 = xl + A, II, J. Number Theory 93 (2002), 183-206.
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0035-0002