Elliptic curves related with triangles
نویسندگان
چکیده
منابع مشابه
Elliptic Curves and Triangles with Three Rational Medians
In his paper Triangles with three rational medians, about the characterization of all rational-sided triangles with three rational medians, Buchholz proves that each such triangle corresponds to a point on a oneparameter family of elliptic curves whose rank is at least 2. We prove that in fact the exact rank of the family in Buchholz paper is 3. We also exhibit a subfamily whose rank is at leas...
متن کاملElliptic curves and related sequences
A Somos 4 sequence is a sequence (hn) of rational numbers defined by the quadratic recursion hm+2 hm−2 = λ1 hm+1 hm−1 + λ2 h 2 m for all m ∈ Z for some rational constants λ1, λ2. Elliptic divisibility sequences or EDSs are an important special case where λ1 = h 2 2, λ2 = −h1 h3, the hn are integers and hn divides hm whenever n divides m. Somos (4) is the particular Somos 4 sequence whose coeffi...
متن کاملRight Triangles with Algebraic Sides and Elliptic Curves over Number Fields
Given any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem. The proof allows the explicit construction of these triangles; for this purpose we find for any positive integer n an explicit cubic number field Q(λ) (depending on n) and an explicit point Pλ of infi...
متن کاملElliptic Curves , Modular Forms and Related
Nick Andersen (University of California, Los Angeles) Kloosterman sums and Maass cusp forms of half-integral weight ABSTRACT: Kloosterman sums play an important role in modern analytic number theory. I will give a brief survey of what is known about the classical Kloosterman sums and their connection to Maass cusp forms of weight 0. I will then talk about recent progress toward bounding sums of...
متن کاملPositivity of Constants Related to Elliptic Curves
Let E be an elliptic curve defined over Q. It is known that the structure of the reduction E(Fp) is (1) E(Fp) ' Z/dpZ⊕ Z/epZ. with dp|ep. The constant
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1996
ISSN: 0386-2194
DOI: 10.3792/pjaa.72.118