On diophantine equations involving sums of powers with quadratic characters as coefficients, II
On discriminants and indices of integers of an algebraic number field.
On divisibility of by the prime
On divisibility of the class number of the real cyclotomic fields by primes
On divisibility of the class number of real octic fields of a prime conductor by
The aim of this paper is to prove the following Theorem Theorem Let be an octic subfield of the field and let be prime. Then divides if and only if divides for some , , , .
On Eigenspaces of the Hecke Algebra with Respect to a Good Maximal Compact Subgroup of ap-Adic Reductive Group.
On Eisenstein's problem
On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields
A large number of papers have contributed to determining the structure of the tame kernel of algebraic number fields F. Recently, for quadratic number fields F whose discriminants have at most three odd prime divisors, 4-rank formulas for have been made very explicit by Qin Hourong in terms of the indefinite quadratic form x² - 2y² (see [7], [8]). We have made a successful effort, for quadratic number fields F = ℚ (√(±p₁p₂)), to characterize in terms of positive definite binary quadratic forms,...
On elementary equivalence, isomorphism and isogeny
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...
On elliptic units and class number of a certain dihedral extension of degree 2l
On Elliptic Units and Class Number of a Certain Non-Galois Number Field.
On embedding numbers into quaternion orders.
On equation in S-units and the Thue-Mahler equation.
On equations in two S-units over function fields of characteristic 0
On equivariant Dedekind zeta-functions at .
On Euclidean rings of integers in cyclotomic fields.
On Euler-von Mangoldt's equation
On Exceptions in the Brauer-Kuroda Relations
Let F be a Galois extension of a number field k with the Galois group G. The Brauer-Kuroda theorem gives an expression of the Dedekind zeta function of the field F as a product of zeta functions of some of its subfields containing k, provided the group G is not exceptional. In this paper, we investigate the exceptional groups. In particular, we determine all nilpotent exceptional groups, and give a sufficient condition for a group to be exceptional. We give many examples of nonnilpotent solvable...
On expansions of Gaussian integers with non-negative digits.
On explicit reciprocity laws. II.