کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8896822 1630623 2018 84 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Non-isotrivial elliptic surfaces with non-zero average root number
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Non-isotrivial elliptic surfaces with non-zero average root number
چکیده انگلیسی
We consider the problem of finding non-isotrivial 1-parameter families of elliptic curves whose root number does not average to zero as the parameter varies in Z. We classify all such families when the degree of the coefficients (in the parameter t) is less than or equal to 2 and we compute the rank over Q(t) of all these families. Also, we compute explicitly the average of the root numbers for some of these families highlighting some special cases. Finally, we prove some results on the possible values average root numbers can take, showing for example that all rational number in [−1,1] are average root numbers for some non-isotrivial 1-parameter family.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 191, October 2018, Pages 1-84
نویسندگان
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