The generalized thue inequality
The Generation of Arithmetical Identities.
The genus class group I
The genus of curves over finite fields with many rational points.
The Genus of Maximal Function Fields over Finite Fields.
The genus of the Barnes-Wall lattice.
The geometry and spectrum of the one holed torus.
The geometry of badly approximable vectors.
The geometry of non-unit Pisot substitutions
It is known that with a non-unit Pisot substitution one can associate certain fractal tiles, so-called Rauzy fractals. In our setting, these fractals are subsets of a certain open subring of the adèle ring of the associated Pisot number field. We present several approaches on how to define Rauzy fractals and discuss the relations between them. In particular, we consider Rauzy fractals as the natural geometric objects of certain numeration systems, in terms of the dual of the one-dimensional realization...
The geometry of the third moment of exponential sums
We give a geometric interpretation (and we deduce an explicit formula) for two types of exponential sums, one of which is the third moment of Kloosterman sums over of type . We establish a connection between the sums considered and the number of -rational points on explicit smooth projective surfaces, one of which is a surface, whereas the other is a smooth cubic surface. As a consequence, we obtain, applying Grothendieck-Lefschetz theory, a generalized formula for the third moment of Kloosterman...
The Gergonne -pile trick and the base counting system. (El truco de pilas de Gergonne y el sistema de numeración de base .)
The GL2 main conjecture for elliptic curves without complex multiplication
Let G be a compact p-adic Lie group, with no element of order p, and having a closed normal subgroup H such that G/H is isomorphic to Zp. We prove the existence of a canonical Ore set S* of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S*, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient of M by its p-primary...
The Golden Section, Fibonacci Series and New Hyperbolic Models of Nature
The Goldston-Pintz-Yıldırım sieve and maximal gaps
The Golomb space is topologically rigid
The Golomb space is the set of positive integers endowed with the topology generated by the base consisting of arithmetic progressions with coprime . We prove that the Golomb space is topologically rigid in the sense that its homeomorphism group is trivial. This resolves a problem posed by T. Banakh at Mathoverflow in 2017.
The greatest common divisor of two recursive functions.
The greatest prime divisor of a product of consecutive integers
The greatest prime factor of
The greatest prime factor of the integers in an interval
The greatest prime factor of the integers in an interval