Hasse Principles in algebraic equations

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.

Representation of prime powers in arithmetical progressions by binary quadratic forms

Franz Halter-Koch (2003)

Journal de théorie des nombres de Bordeaux

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Let $Γ$ be a set of binary quadratic forms of the same discriminant, $Δ$ a set of arithmetical progressions and $m$ a positive integer. We investigate the representability of prime powers $p^{m}$ lying in some progression from $Δ$ by some form from $Γ$ .

An application of dihedral fields to representations of primes by binary quadratic forms

Pierre Kaplan, Kenneth Williams, Yoshihiko Yamamoto (1984)

Acta Arithmetica

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Arithmetic euclidean rings

Clifford Queen (1974)

Acta Arithmetica

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On a theorem of Bauer and some of its applications

Andrzej Schinzel (1966)

Acta Arithmetica

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