Computing the average root number of an elliptic surface
نویسندگان
چکیده
منابع مشابه
Average Root Numbers in Families of Elliptic Curves
We introduce a height measure on Q to count rational numbers. Through it, we prove a density result on the average value of the root numbers of families of twists of elliptic curves. Zagier and Kramarz computed in [11] the rank of the curves x + y = m, with m an integer < 70, 000. These data suggest that the rank is even for exactly half of the twists of x + y = 1. This conjecture has been prov...
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Nagao has recently given a conjectural limit formula for the rank of an elliptic surface E in terms of a weighted average of bral Frobenius trace values. We show that Tate's conjecture on the order of vanishing of L 2 (E; s) essentially implies Nagao's formula; in particular, we prove Nagao's formula for rational elliptic surfaces. In the case that E is a twist, we reduce Nagao's and Tate's con...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2019
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2018.07.012