Arithmetic Clifford's theorem for Hermitian vector bundles
Arithmetic cycles on Picard modular surfaces and modular forms of Nebentypus.
Arithmetic differential equations in several variables
We survey recent work on arithmetic analogues of ordinary and partial differential equations.
Arithmetic diophantine approximation for continued fractions-like maps on the interval
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the fractional part of Möbius transformations which carry the end points of the unit interval to zero and infinity, extending the classical regular and backwards continued fraction expansions.
Arithmetic Distance Functions and Height Fuctions in Diophantine Geometry.
Arithmetic euclidean rings
Arithmetic Fuchsian groups and the number of systoles.
Arithmetic functions and weighted averages
Arithmetic functions associated with the infinitary divisors of an integer.
Arithmetic functions on Beatty sequences
Arithmetic functions over rings with zero divisors.
Arithmetic Gevrey series and transcendence. A survey
We review the main results of the theory of arithmetic Gevrey series introduced in [3] [4], their applications to transcendence, and a few diophantine conjectures on the summation of divergent series.
Arithmetic groups and salem numbers.
Arithmetic Hilbert modular functions (II).
The purpose of this paper, which is a continuation of [2, 3], is to prove further results about arithmetic modular forms and functions. In particular we shall demonstrate here a q-expansion principle which will be useful in proving a reciprocity law for special values of arithmetic Hilbert modular functions, of which the classical results on complex multiplication are a special case. The main feature of our treatment is, perhaps, its independence of the theory of abelian varieties.
Arithmetic hyperbolic surface bundles.
Arithmetic implications of the distribution of integral zeros of exponential polynomials
Arithmetic infinite Grassmannians and the induced central extensions.
Arithmetic of 0-cycles on varieties defined over number fields
Let be a rationally connected algebraic variety, defined over a number field We find a relation between the arithmetic of rational points on and the arithmetic of zero-cycles. More precisely, we consider the following statements: (1) the Brauer-Manin obstruction is the only obstruction to weak approximation for -rational points on for all finite extensions (2) the Brauer-Manin obstruction is the only obstruction to weak approximation in some sense that we define for zero-cycles of degree...
Arithmetic of an elliptic curve and circle actions on four-manifolds
Arithmetic of block monoids