Good Lattice Points Modulo Composite Numbers.
Good lower and upper bounds on binomial coefficients.
Good reduction of affinoids on the Lubin-Tate tower.
Good reduction of elliptic curves in abelian extensions.
Good reduction of elliptic curves over imaginary quadratic fields
We prove that the -invariant of an elliptic curve defined over an imaginary quadratic number field having good reduction everywhere satisfies certain Diophantine equations under some hypothesis on the arithmetic of the quadratic field. By solving the Diophantine equations explicitly in the rings of quadratic integers, we show the non-existence of such elliptic curve for certain imaginary quadratic fields. This extends the results due to Setzer and Stroeker.
Gosset polytopes in integral octonions
We study the integral quaternions and the integral octonions along the combinatorics of the -cell, a uniform polytope with the symmetry , and the Gosset polytope with the symmetry . We identify the set of the unit integral octonions or quaternions as a Gosset polytope or a -cell and describe the subsets of integral numbers having small length as certain combinations of unit integral numbers according to the or actions on the or the -cell, respectively. Moreover, we show that each...
Governing fields for the 2-classgroup of and a related reciprocity law
Graceful numbers.
Graded algebra automorphisms.
Graded quaternion symbol equivalence of function fields
We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.
Graded Witt Rings of Elementary Type.
Gram's Law and the Argument of the Riemann Zeta Function
Grandes valeurs des fonctions arithmétiques
Grandes valeurs d'une fonction liée au produit d'entiers consécutifs
Grands degrés de transcendance pour la fonction exponentielle ; modification des hypothèses techniques dans la méthode de Brownawell
Grands degrés de transcendance pour la fonction exponentielle ; modification des hypothèses techniques dans la méthode de Diaz
Graphes de Ramanujan et applications
Gravity, strings, modular and quasimodular forms
Modular and quasimodular forms have played an important role in gravity and string theory. Eisenstein series have appeared systematically in the determination of spectrums and partition functions, in the description of non-perturbative effects, in higher-order corrections of scalar-field spaces, ...The latter often appear as gravitational instantons i.e. as special solutions of Einstein’s equations. In the present lecture notes we present a class of such solutions in four dimensions, obtained by...
Greatest common divisors in shifted Fibonacci sequences.
Greatest common divisors of , in positive characteristic and rational points on curves over finite fields
In our previous work we proved a bound for the , for -units of a function field in characteristic zero. This generalized an analogous bound holding over number fields, proved in [3]. As pointed out by Silverman, the exact analogue does not work for function fields in positive characteristic. In the present work, we investigate possible extensions in that direction; it turns out that under suitable assumptions some of the results still hold. For instance we prove Theorems 2 and 3 below, from...