کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8899869 | 1631552 | 2018 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A parametrization of θ-congruent numbers with many prime factors and with prescribed prime factors
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let θ be a real number such that 0<θ<Ï and cosâ¡Î¸âQ. For each positive integer n, we give a parametrization Sn(α) whose square-free part Nn(α) for each negative integer α is a θ-congruent number with many prime factors including any given primes (especially, at least n prime factors that are guaranteed to appear) by showing the positivity of the rank of the corresponding θ-congruent number elliptic curve over Q. Especially, we show that if a given odd prime p>2n is near 2n, then p appears as a factor of Nn(α) very often as α varies all over negative integers by proving that the probability of the set of all negative integers α such that p divides Nn(α) is 2n+1p+1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 462, Issue 1, 1 June 2018, Pages 407-427
Journal: Journal of Mathematical Analysis and Applications - Volume 462, Issue 1, 1 June 2018, Pages 407-427
نویسندگان
Bo-Hae Im, Hansol Kim,