A mean value theorem of Bombieri's type
Abschätzungen für die Funktion ... (x,y) in algebraischen Zahlkörpern.
An interval result for the number field v(x,y) function.
Artin's conjecture in algebraic number fields and a related question concerning units
Artin's primitive root conjecture for quadratic fields
Fix an element in a quadratic field . Define as the set of rational primes , for which has maximal order modulo . Under the assumption of the generalized Riemann hypothesis, we show that has a density. Moreover, we give necessary and sufficient conditions for the density of to be positive.
Chebotarev sets
We consider the problem of determining whether a set of primes, or, more generally, prime ideals in a number field, can be realized as a finite union of residue classes, or of Frobenius conjugacy classes. We give necessary conditions for a set to be realized in this manner, and show that the subset of primes consisting of every other prime cannot be expressed in this way, even if we allow a finite number of exceptions.
Chebyshev's bias.
Chebyshev's method for number fields
We give an elementary proof of an explicit estimate for the number of primes splitting completely in an extension of the rationals. The proof uses binomial coefficents and extends Chebyshev's classical approach.
Ein Analogin zum Primzahlsatz für algebraische Funktionenkörper.
Lefschetz trace formulas and explicit formulas in analytic number theory.
Linear forms and arithmetic equivalence
Non-unique factorizations in block semigroups and arithmetical applications
On an additive function on the set of ideals of an arbitrary number field
On Euler-von Mangoldt's equation
On ideals free of large prime factors
In 1989, E. Saias established an asymptotic formula for with a very good error term, valid for , , We extend this result to an algebraic number field by obtaining an asymptotic formula for the analogous function with the same error term and valid in the same region. Our main objective is to compare the formulae for and and in particular to compare the second term in the two expansions.
On the distribution of norms of prime ideals of a given class in arithmetic progressions.
On the number of sign changes in the remainder-term of the prime-ideal theorem
On the Piltz divisor problem in algebraic number fields
The least prime which does not split completely.
The Normal Density of Prime Ideals in Small Regions.