Displaying similar documents to “Representation of prime powers in arithmetical progressions by binary quadratic forms”

Artin's primitive root conjecture for quadratic fields

Hans Roskam (2002)

Journal de théorie des nombres de Bordeaux

Similarity:

Fix an element α in a quadratic field K . Define S as the set of rational primes p , for which α has maximal order modulo p . Under the assumption of the generalized Riemann hypothesis, we show that S has a density. Moreover, we give necessary and sufficient conditions for the density of S to be positive.

On the prime density of Lucas sequences

Pieter Moree (1996)

Journal de théorie des nombres de Bordeaux

Similarity:

The density of primes dividing at least one term of the Lucas sequence L n ( P ) n = 0 ∞ , defined by L 0 ( P ) = 2 , L 1 ( P ) = P and L n ( P ) = P L n - 1 ( P ) + L n - 2 ( P ) for n ≥ 2 , with P an arbitrary integer, is determined.

Weber's class invariants revisited

Reinhard Schertz (2002)

Journal de théorie des nombres de Bordeaux

Similarity:

Let K be a quadratic imaginary number field of discriminant d . For t ∈ ℕ let 𝔒 t denote the order of conductor t in K and j ( 𝔒 t ) its modular invariant which is known to generate the ring class field modulo t over K . The coefficients of the minimal equation of j ( 𝔒 t ) being quite large Weber considered in [We] the functions f , f 1 , f 2 , γ 2 , γ 3 defined below and thereby obtained simpler generators of the ring class fields. Later on the singular values of these functions played a crucial role in Heegner’s solution [He] of...

On the 2-primary part of K₂ of rings of integers in certain quadratic number fields

A. Vazzana (1997)

Acta Arithmetica

Similarity:

1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of K ₂ E . 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 ℚ ( √ ( p ₁ . . . p k ) ) , where the primes p i 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 K ₂ E is zero for such fields. In the course...

On 2 -class field towers of imaginary quadratic number fields

Franz Lemmermeyer (1994)

Journal de théorie des nombres de Bordeaux

Similarity:

For a number field k , let k 1 denote its Hilbert 2 -class field, and put k 2 = ( k 1 ) 1 . We will determine all imaginary quadratic number fields k such that G = G a l ( k 2 / k ) is abelian or metacyclic, and we will give G in terms of generators and relations.

On integral representations by totally positive ternary quadratic forms

Elise Björkholdt (2000)

Journal de théorie des nombres de Bordeaux

Similarity:

Let K be a totally real algebraic number field whose ring of integers R is a principal ideal domain. Let f ( x 1 , x 2 , x 3 ) be a totally definite ternary quadratic form with coefficients in R . We shall study representations of totally positive elements N ∈ R by f . We prove a quantitative formula relating the number of representations of N by different classes in the genus of f to the class number of R [ - c f N ] , where c f ∈ R is a constant depending only on f . We give an algebraic proof of a classical result of H. Maass...