A Bound for the Least Prime Ideal in the Chebotarev Density Theorem.
A new equidistribution property of norms of ideals in given classes
A note on the torsion of the Jacobians of superelliptic curves
This article is a short version of the paper published in J. Number Theory 145 (2014) but we add new results and a brief discussion about the Torsion Conjecture. Consider the family of superelliptic curves (over ℚ) , and its Jacobians , where 2 < q < p are primes. We give the full (resp. partial) characterization of the torsion part of (resp. ). The main tools are computations of the zeta function of (resp. ) over for primes l ≡ 1,2,4,8,11 (mod 15) (resp. for primes l ≡ -1 (mod qp))...
A purely algebraic proof of special cases of Tchebotarev's theorem
An effective estimate for the density of zeros of Hecke-Landau zeta-functions
An effective order of Hecke-Landau zeta functions near the line σ=1, II (some applications)
Artin's conjecture on primes with prescribed primitive roots
Asymptotically exact heuristics for prime divisors of the sequence .
Average r-rank Artin conjecture
Let Γ ⊂ ℚ * be a finitely generated subgroup and let p be a prime such that the reduction group Γₚ is a well defined subgroup of the multiplicative group ₚ*. We prove an asymptotic formula for the average of the number of primes p ≤ x for which [ₚ*:Γₚ] = m. The average is taken over all finitely generated subgroups , with and , with a range of uniformity for every i = 1,...,r. We also prove an asymptotic formula for the mean square of the error terms in the asymptotic formula with a similar...
Computing higher rank primitive root densities
We extend the "character sum method" for the computation of densities in Artin primitive root problems given by Lenstra and the authors to the situation of radical extensions of arbitrary rank. Our algebraic set-up identifies the key parameters of the situation at hand, and obviates the lengthy analytic multiplicative number theory arguments that used to go into the computation of actual densities. It yields a conceptual interpretation of the formulas obtained, and enables us to extend their range...
Contributions to the theory of Kummer extensions
Correction to the paper "Densities for 3-class ranks of pure cubic fields", Acta Arith 46 (1986), pp. 227-242
Counting certain number fields with prescribed l-class numbers.
Counting cyclic quartic extensions of a number field
In this paper, we give asymptotic formulas for the number of cyclic quartic extensions of a number field.
Counting discriminants of number fields
For each transitive permutation group on letters with , we give without proof results, conjectures, and numerical computations on discriminants of number fields of degree over such that the Galois group of the Galois closure of is isomorphic to .
Densities for 3-class ranks in certain cubic extensions.
Densities for 3-class ranks of pure cubic fields
Densities for certain -ranks in cyclic fields of degree
Densities of 4-ranks of K₂(𝒪)
Density modulo 1 in local fields