Ideal Matrices and Ideal Vectors.
Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients
We consider the indices of subfields of cyclotomic ℤₚ-extensions of number fields. For the nth layer Kₙ of the cyclotomic ℤₚ-extension of ℚ, we find that the prime factors of the index of Kₙ/ℚ are those primes less than the extension degree pⁿ which split completely in Kₙ. Namely, the prime factor q satisfies , and this leads us to consider higher degree Fermat quotients. Indices of subfields of cyclotomic ℤₚ-extensions of a number field which is cyclic over ℚ with extension degree a prime different...
Infinite product representations in complex quadratic fields
Initial layers of -extensions of complex quadratic fields
Integral bases in algebraic number fields.
Irregular imaginary fields
Isomorphisms of algebraic number fields
Let and be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, . The algorithm is particularly efficient if there is only one isomorphism.