On the analogue of the formula of Chowla and Selberg for real quadratic fields.
On the anticyclotomic main conjecture for CM fields.
On the arithmetic of an elliptic curve over a -extension
On the arithmetic of cross-ratios and generalised Mertens’ formulas
We develop the relation between hyperbolic geometry and arithmetic equidistribution problems that arises from the action of arithmetic groups on real hyperbolic spaces, especially in dimension . We prove generalisations of Mertens’ formula for quadratic imaginary number fields and definite quaternion algebras over , counting results of quadratic irrationals with respect to two different natural complexities, and counting results of representations of (algebraic) integers by binary quadratic, Hermitian...
On the arithmetic of quaternion algebras
On the arithmetic of some division algebras.
On the Arithmetic of Special Values of L Functions.
On the arithmetic of two constructions of Salem numbers.
On the asymptotic behavior of some counting functions
The investigation of certain counting functions of elements with given factorization properties in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group. In this paper a constant arising from the investigation of the number of algebraic integers with factorizations of at most k different lengths is investigated. It is shown that this constant is positive if k is greater than 1 and that it is also positive if k equals 1 and the class group satisfies...
On the asymptotic behavior of some counting functions, II
The investigation of the counting function of the set of integral elements, in an algebraic number field, with factorizations of at most k different lengths gives rise to a combinatorial constant depending only on the class group of the number field and the integer k. In this paper the value of these constants, in case the class group is an elementary p-group, is estimated, and determined under additional conditions. In particular, it is proved that for elementary 2-groups these constants are equivalent...
On the Asymptotic Behaviour of the Ideal Counting Function in Quadratic Number Fields.
On the Behaviour of p-Adic L-Functions at s= 0.
On the branch order of the ring of integers of an abelian number field
On the canonical height for the algebraic unit group.
On the center of Galois groups of maximal pro-p extensions of algebraic number fields with restricted ramification.
On the class number of relative abelian fields.
On the class number of some real abelian number fields of prime conductors
On the class number of the maximal real subfields of a family of cyclotomic fields
For any square-free positive integer with , we prove that the class number of the real cyclotomic field is greater than , where is a primitive th root of unity.
On the class number Q(√-p) modulo 16, for p ≡ 1 (mod 8) a prime
On the class numbers of certain Hilbert class fields.