On some new estimates for h¯(ℚ(ζₚ))
On some polynomials allegedly related to the abc conjecture
On some truncated units in algebraic number fields of degree n ... 3.
On special values of theta functions of genus two
We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.
On Sums of Squares in etc
On S-unit equations in two unknowns.
On supercharacter theoretic generalizations of monomial groups and Artin's conjecture
We extend the notions of quasi-monomial groups and almost monomial groups in the framework of supercharacter theories, and we study their connection with Artin’s conjecture regarding the holomorphy of Artin -functions.
On Sylow 2-subgroups of K2OF for quadratic number fields F.
On symmetric and unsymmetric theta functions over a real quadratic field
On Tate’s refinement for a conjecture of Gross and its generalization
We study Tate’s refinement for a conjecture of Gross on the values of abelian -function at and formulate its generalization to arbitrary cyclic extensions. We prove that our generalized conjecture is true in the case of number fields. This in particular implies that Tate’s refinement is true for any number field.
On Tate-Shafarevich groups of .
On Taylor's conjecture for Kummer orders
On the -class group of some number fields with large degree
Let be an odd square-free integer, any integer and . In this paper, we shall determine all the fields having an odd class number. Furthermore, using the cyclotomic -extensions of some number fields, we compute the rank of the -class group of whenever the prime divisors of are congruent to or .
On the 2-primary part of a conjecture of Birch and Tate
On the 2-primary part of K₂ of rings of integers in certain quadratic number fields
1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of . For quadratic fields whose discriminant has arbitrarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form , where the primes are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrelbrink which examines under what conditions the 4-rank of is zero for such fields. In the course of proving...
On the 2-Sylow subgroup of the Hilbert kernel of of number fields
On the 3-class field tower of some biquadratic fields
On the 4-rank of ideal class groups of quadratic function fields
On the 4-rank of tame kernels of quadratic number fields
On the Action of the Frobenius Automorphism on the Pro-l Fundamental Group.