Generators and defining equation of the modular function field of the group Γ₁(N)
Generators and equations for modular function fields of principal congruence subgroups
Generators and integer points on the elliptic curve y² = x³ - nx
Let E be an elliptic curve over the rationals ℚ given by y² = x³ - nx with a positive integer n. We consider first the case where n = N² for a square-free integer N. Then we show that if the Mordell-Weil group E(ℚ ) has rank one, there exist at most 17 integer points on E. Moreover, we show that for some parameterized N a certain point P can be in a system of generators for E(ℚ ), and we determine the integer points in the group generated by the point P and the torsion points. Secondly, we consider...
Generators and integral points on twists of the Fermat cubic
We study integral points and generators on cubic twists of the Fermat cubic curve. The main results assert that integral points can be in a system of generators in the case where the Mordell-Weil rank is at most two. As a corollary, we explicitly describe the integral points on the curve.
Generators for nonlinear three term recurrences involving the greatest integer function.
Generators for the elliptic curve
Let be an elliptic curve given by with a positive integer . Duquesne in 2007 showed that if is square-free with an integer , then certain two rational points of infinite order can always be in a system of generators for the Mordell-Weil group of . In this paper, we generalize this result and show that the same is true for infinitely many binary forms in .
Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture
We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of -kernel.
Generic points in the cartesian powers of the Morse dynamical system
The symbolic dynamical system associated with the Morse sequence is strictly ergodic. We describe some topological and metrical properties of the Cartesian powers of this system, and some of its other self-joinings. Among other things, we show that non generic points appear in the fourth power of the system, but not in lower powers. We exhibit various examples and counterexamples related to the property of weak disjointness of measure preserving dynamical systems.
Genre arithmétique des groupes modulaires de Hilbert et nombres de classes de quaternions.
Genre et genre residuel des corps de fonctions values.
Genre et genre résiduel des corps de fonctions valués
Genres de Todd et valeurs aux entiers des dérivées de fonctions
La géométrie d’Arakelov étudie les fibrés vectoriels sur une variété algébrique définie sur les entiers, munis d’une métrique hermitienne lisse sur le fibré holomorphe associé (sur la variété analytique des points complexes de ). Un théorème de “Riemann-Roch arithmétique” calcule le covolume du réseau euclidien des sections globales d’un tel fibré. Dans cette formule, le genre de Todd comporte un terme complémentaire, défini par une série formelle dont les coefficients font intervenir les valeurs...
Genus number and l-Rank of Genus Group of cyclic extensions of Degree l.
Genus one curves defined by separated variable polynomials and a polynomial Pell equation
Genus zero translates of three point ramified Galois extensions.
Geodesic cycles and the Weil representation I ; quotients of hyperbolic space and Siegel modular forms
Geodesics on Riemann surfaces with ramification points of order greater than two.
Geometric and -adic Modular Forms of Half-Integral Weight
In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define -adic modular forms of half-integral weight and to construct -adic Hecke operators.
Geometric aspect of Weyl sums
Geometric description of the connecting homomorphism for Witt groups.