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Zbl 0878.14028
Manduchi, Elisabetta
Root numbers of fibers of elliptic surfaces. (English)
[J] Compos. Math. 99, No.1, 33-58 (1995). ISSN 0010-437X; ISSN 1570-5846/e

Summary: The variation of the root number on fibers of elliptic surfaces over the rationals with base the projective line is studied. It is proved that for a large class of such surfaces the sets of rational $t$'s such that the fiber over $t$ is an elliptic curve with root number 1 and $-1$ respectively are both dense in the set of real numbers. This result provides some evidence for a recent conjecture of {\it B. Mazur} [see Exp. Math. 1, No. 1, 35-45 (1992; Zbl 0784.14012)]. A similar result and some applications are also discussed.

MSC 2000:: *14J27 Elliptic surfaces
14D99 Families, fibrations

Keywords: root number; fibers of elliptic surfaces

Citations: Zbl 0784.14012

Cited in: Zbl 0901.14020

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