Results 41 to 50 of about 2,036 (63)
Integer Triangles with R/r=N [PDF]
arXiv, 2005 We consider the problem of finding integer-sided triangles with R/r an integer, where R and r are the radii of the circumcircle and incircle respectively. We show that such triangles are relatively rare.
arxiv
A Shafarevich-Faltings Theorem For Rational Functions [PDF]
arXiv, 2006 Using an alternative notion of good reduction, an analog of the Shafarevich theorem for elliptic curves is proved for morphisms of the projective line over number fields.
arxiv
Square Eulerian Quadruples [PDF]
arXiv, 2006 We consider the problem of finding 4 rational squares, such that the product of any two plus the sum of the same two always gives a square. We give some historical background and exhibit one such quadruple.
arxiv
Local torsion on elliptic curves and the deformation theory of Galois representations [PDF]
arXiv, 2007 We prove that, on average, elliptic curves over Q have finitely many primes p for which they possess a p-adic point of order p. We include a discussion of applications to companion forms and the deformation theory of Galois representations.
arxiv
On the Mordell-Weil lattice of y 2 = x 3 + b x + t 3 n + 1 in characteristic 3. [PDF]
Res Number Theory, 2022 Leterrier G.
europepmc +1 more source
Defining equations of $X_0(2^{2n})$ [PDF]
arXiv, 2007 In this note we obtain defining equations of modular curves $X_0(2^{2n})$. The key ingredient is a recursive formula for certain generators of the function fields on $X_0(2^{2n})$.
arxiv
Orienteering with One Endomorphism. [PDF]
Mathematica (N Y), 2023 Arpin S +5 more
europepmc +1 more source
Primitive divisors on twists of the Fermat cubic [PDF]
arXiv, 2007 We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, u^3+v^3=m, with m cube-free, all the terms beyond the first have a primitive divisor.
arxiv
A complete diophantine characterization of the rational torsion of an elliptic curve [PDF]
arXiv, 2007 We give a complete characterization for the rational torsion of an elliptic curve in terms of the (non-)existence of integral solutions of a system of diophantine equations.
arxiv
Power-free values, repulsion between points, differing beliefs and the existence of error [PDF]
arXiv, 2007 Let f be a cubic polynomial. Then there are infinitely many primes p such that f(p) is square-free.
arxiv