کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4594007 | 1335736 | 2013 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On uniform bounds for rational points on rational curves of arbitrary degree
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We show that for any ϵ>0 the number of rational points of height less than B on the image of a degree d map from P1 to P2 is bounded above by CdB2/d+d2, where the point is that for fixed d the constant Cd is independent of the choice of map. This improves on a result of Heath-Brown, which states that for any ϵ>0 the number of rational points of height less than B on a degree d plane curve is Od,ϵ(B2/d+ϵ). It is known that Heath-Brownʼs theorem is sharp apart from the ϵ; our results show that for our degree d rational curves it is true with ϵ=0.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 133, Issue 9, September 2013, Pages 3112-3118
Journal: Journal of Number Theory - Volume 133, Issue 9, September 2013, Pages 3112-3118
نویسندگان
Patrick X. Rault,