A growth bound on the partial quotients of cubic numbers.
A Grunwald-Wang type theorem for abelian varieties
A “Hardy-Littlewood” approach to the -unit equation
A Hasse principle for two dimensional global fields.
A Hauptsatz of L. E. Dickson and Artin-Schreier extensions.
A Higher Dimensional Analogue of Mordell's Conjecture Over Function Fields.
A higher rank Selberg sieve and applications
We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.
A hybrid mean value involving two-term exponential sums and polynomial character sums
Let be a positive integer. For any integers and , the two-term exponential sum is defined by , where . In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.
A hybrid mean value of the Dedekind sums
The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
A hybrid mean value related to certain Hardy sums and Kloosterman sums
The main purpose of this paper is using the mean value formula of Dirichlet L-functions and the analytic methods to study a hybrid mean value problem related to certain Hardy sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.
A hybrid mean value related to Dedekind sums
The main purpose of this paper is to study a hybrid mean value problem related to the Dedekind sums by using estimates of character sums and analytic methods.
A hybrid of theorems of Goldbach and Piatetski-Shapiro
A Hyperbolic Kac-Moody Algebra and the Theory of Siegel Modular Forms of Genus 2.
A hyperelliptic diophantine equation related to imaginary quadratic number fields with class number 2.
A hyperelliptic diophantine equation related to imaginary quadratic number fields with class number 2.
A Joint Universality Theorem for Dirichlet L-Functions.
A Kronecker Limit Formula for Real Quadratic Fields.
A Kummer criterion for imaginary quadratic fields
A Kuzmin theorem for a class of number theoretic endomorphisms
À la recherche de petites sommes d'exponentielles
Soit une fraction rationnelle à coefficients entiers, vérifiant des hypothèses assez générales. On prouve l’existence d’une infinité d’entiers , ayant exactement deux facteurs premiers, tels que la somme d’exponentielles soit en , où est une constante ne dépendant que de la géométrie de . On donne aussi des résultats de répartition du type Sato-Tate, pour certaines sommes de Salié, modulo , avec entier comme ci- dessus.