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
Arithmetic of certain hypergeometric modular forms
Arithmetic of cyclic quotients of the Fermat quintic
Arithmetic of elliptic curves and diophantine equations
We give a survey of methods used to connect the study of ternary diophantine equations to modern techniques coming from the theory of modular forms.
Arithmetic of elliptic curves with supersingular reduction in . (Arithmétique des courbes elliptiques à réduction supersingulière en .)
Arithmetic of formal groups and applications I: Universal norm subgroups.
Arithmetic of half integral weight theta-series
Arithmetic of Hermitian forms.
Arithmetic of linear forms involving odd zeta values
A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of and , as well as to explain Rivoal’s recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers , , , and is irrational.
Arithmetic of non-principal orders in algebraic number fields
Let be an order in an algebraic number field. If is a principal order, then many explicit results on its arithmetic are available. Among others, is half-factorial if and only if the class group of has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.
Arithmetic of Pell surfaces
Arithmetic of quaternary quadratic forms
Arithmetic of the modular function
We find a generator of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
Arithmetic on blocks.
Arithmetic on elliptic curves with complex multiplication. II.