"Almost every" algebraic number-field has a large class-number
Amélioration d'une congruence pour certains éléments de Stickelberger quadratiques
An absolute Siegel's Lemma.
An adelic Minkowski-Hlawka theorem and an application to Siegel's lemma.
An Algebraic Approach to the Residues in Algebraic Geometry.
An algorithm for finding an algebraic number whose norm is a given rational number.
An algorithmic construction of cyclic p-extensions of fields, with characteristic different from p, not containing the pth roots of unity
An analogue in certain unique factorization domains of the Euclid-Euler theorem on perfect numbers.
An Analogue of Artin-Schreier Theorem.
An analogue of class-number in higher dimensions.
An Analogue of Stickelberger's Theorem for the Higher K-Groups.
An annihilator for the -Selmer group by means of Heegner points
Let be a modular elliptic curve, and let be an imaginary quadratic field. We show that the -Selmer group of over certain finite anticyclotomic extensions of , modulo the universal norms, is annihilated by the «characteristic ideal» of the universal norms modulo the Heegner points. We also extend this result to the anticyclotomic -extension of . This refines in the current contest a result of [1].
An Application of a Theorem of Deuring and Safarevic.
An application of dihedral fields to representations of primes by binary quadratic forms
An application of the Kronecker limit formula.
An application of the p-adic class number formula.
An arithmetic analogue of Clifford's theorem.
An arithmetic analogue of Clifford's theorem
Number fields can be viewed as analogues of curves over fields. Here we use metrized line bundles as analogues of divisors on curves. Van der Geer and Schoof gave a definition of a function on metrized line bundles that resembles properties of the dimension of , where is a divisor on a curve . In particular, they get a direct analogue of the Rieman-Roch theorem. For three theorems of curves, notably Clifford’s theorem, we will propose arithmetic analogues.
An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation
An arithmetic problem on the sums of three squares