On a direct sum decomposition of the Dem'yanenko matrix
On a problem of Eisenstein
On a ratio between relative class numbers.
On algebraic number fields with even class numbers.
On annihilators of the class group of an imaginary compositum of quadratic fields
On CM-fields with the same maximal real subfield
On congruent primes and class numbers of imaginary quadratic fields
We consider the problem of determining whether a given prime p is a congruent number. We present an easily computed criterion that allows us to conclude that certain primes for which congruency was previously undecided, are in fact not congruent. As a result, we get additional information on the possible sizes of Tate-Shafarevich groups of the associated elliptic curves. We also present a related criterion for primes p such that divides the class number of the imaginary quadratic field ℚ(√-p)....
On cyclotomic ℤ ₚ-extensions of real quadratic fields
On -polynomials with integer coefficients
We give a family of -polynomials with integer coefficients whose splitting fields over are unramified cyclic quintic extensions of quadratic fields. Our polynomials are constructed by using Fibonacci, Lucas numbers and units of certain cyclic quartic fields.
On diophantine equations involving sums of powers with quadratic characters as coefficients, II
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 Elliptic Units and Class Number of a Certain Non-Galois Number Field.
On Euclidean rings of integers in cyclotomic fields.
On ideal groups of algebraic number fields.
On Imaginary abelian number fields of type (2, 2, ..., 2) with one class in each genus.
On index formulas of Siegel units in a ring class field
On Jacobi sums in ℚ(ζₚ)
On non-abelian Stark-type conjectures
We introduce non-abelian generalizations of Brumer’s conjecture, the Brumer-Stark conjecture and the strong Brumer-Stark property attached to a Galois CM-extension of number fields. Moreover, we discuss how they are related to the equivariant Tamagawa number conjecture, the strong Stark conjecture and a non-abelian generalization of Rubin’s conjecture due to D. Burns.