On Gauss sum characters of finite groups and generalized Bernoulli numbers
On general L-functions
On Geometric Zp-Extensions of Function Fields.
On Grunwald-Wang's theorem.
On Hilbert-Speiser type imaginary quadratic fields
On Hirzebruch sums and a theorem of Schinzel
On ideal groups of algebraic number fields.
On ideals free of large prime factors
In 1989, E. Saias established an asymptotic formula for with a very good error term, valid for , , We extend this result to an algebraic number field by obtaining an asymptotic formula for the analogous function with the same error term and valid in the same region. Our main objective is to compare the formulae for and and in particular to compare the second term in the two expansions.
On Imaginary abelian number fields of type (2, 2, ..., 2) with one class in each genus.
On indecomposable quadratic forms.
On index formulas of Siegel units in a ring class field
On integer solutions to x² - dy² = 1, z² - 2dy² =1
On integral normal bases over intermediary fields
On integral representations by totally positive ternary quadratic forms
Let be a totally real algebraic number field whose ring of integers is a principal ideal domain. Let be a totally definite ternary quadratic form with coefficients in . We shall study representations of totally positive elements by . We prove a quantitative formula relating the number of representations of by different classes in the genus of to the class number of , where is a constant depending only on . We give an algebraic proof of a classical result of H. Maass on representations...
On integral Stark conjectures (and multiplicative Galois module structures).
On intervals containing full sets of conjugates of algebraic integers
On invariants related to non-unique factorizations in block monoids and rings of algebraic integers
On Iwasawa’s λ-invariant for certain -extensions
On Jacobi sums in ℚ(ζₚ)
On Jannsen's conjecture for Hecke characters of imaginary quadratic fields.
We present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic field K of class number 1.The conjecture is easy to check for Galois groups purely of local type (Section 1). In Section 2 we define the p-adic realizations associated to Hecke characters over K. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field K at p, which is related to the property that a global Galois...