On algebraic curves $$A(x)-B(y)=0$$ A ( x ) - B ( y ) = 0 of genus zero
نویسندگان
چکیده
منابع مشابه
Pairing - friendly Hyperelliptic Curves of Type y 2 = x 5 + ax
An explicit construction of pairing-friendly hyperelliptic curves with ordinary Jacobians was firstly given by D. Freeman. In this paper, we give other explicit constructions of pairing-friendly hyperelliptic curves. Our methods are based on the closed formulae for the order of the Jacobian of a hyperelliptic curve of type y = x + ax over a finite prime field Fp which are given by E. Furukawa, ...
متن کاملA Generalized Fibonacci Sequence and the Diophantine Equations $x^2pm kxy-y^2pm x=0$
In this paper some properties of a generalization of Fibonacci sequence are investigated. Then we solve the Diophantine equations $x^2pmkxy-y^2pm x=0$, where $k$ is positive integer, and describe the structure of solutions.
متن کاملOn the Elliptic Curves of the Form $y^2 = x^3 − pqx$
By the Mordell- Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves, where p and q are distinct primes. We give infinite families of elliptic curves of the form y2=x3-pqx with rank two, three and four, assuming a conjecture of Schinzel ...
متن کاملOn the elliptic curves of the form $ y^2=x^3-3px $
By the Mordell-Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. There is no known algorithm for finding the rank of this group. This paper computes the rank of the family $ E_p:y^2=x^3-3px $ of elliptic curves, where p is a prime.
متن کامل• For all x ∈ R n, x T Ax ≥ 0.
Notation: The set of real symmetric n ×n matrices is denoted S . A matrix A ∈ S is called positive semidefinite if x Ax ≥ 0 for all x ∈ R, and is called positive definite if x Ax > 0 for all nonzero x ∈ R . The set of positive semidefinite matrices is denoted S and the set of positive definite matrices + n is denoted by S++. The cone S is a proper cone (i.e., closed, convex, pointed, and solid). +
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: Mathematische Zeitschrift
سال: 2017
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-017-1889-9