Corrigendum to the paper "On the 2-primary part of a conjecture of Birch and Tate" (Acta Arith. 43 (1983), 69-81)
Corrigendum to the paper "On the distribution of s-dimensional Kronecker sequences" Acta Arith. 51 (1988), 335-347
Corrigendum to the paper "On the probability that n and f(n) are relatively prime"
Corrigendum to the paper "Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory"
Corrigendum to the paper "The number of solutions of the Mordell equation" (Acta Arith. 88 (1999), 173–179)
Corrigendum to Theorem 5 of the paper "Asymptotic density of A ⊂ ℕ and density of the ratio set R(A) (Acta Arith. 87 (1998), 67-78)
Corrigendum zu: ?Invarianten endlicher Gruppen und biholomorphe Abbildungen". Inventiones math. 6, 315 - 326 (1969).
Corrigendum zur Arbeit „Über die reellen Nullstellen der Dirichletschen L-Reihen"
Counting all equilateral triangles in .
Counting certain number fields with prescribed l-class numbers.
Counting colorings on varieties.
We present a combinatorial mechanism for counting certain objects associated to a variety over a finite field. The basic example is that of counting conjugacy classes of the general linear group. We discuss how the method applies to counting these and also to counting unipotent matrices and pairs of commuting matrices.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
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 determinants of Fibonacci-Hessenberg matrices using LU factorizations.
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 .
Counting distinct zeros of the Riemann zeta-function.
Counting elliptic curves of bounded Faltings height
We give an asymptotic formula for the number of elliptic curves over ℚ with bounded Faltings height. Silverman (1986) showed that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in ℝ².
Counting exceptional units.
Counting functions and finite differences.
Counting invertible matrices and uniform distribution
Consider the group over the ring of algebraic integers of a number field . Define the height of a matrix to be the maximum over all the conjugates of its entries in absolute value. Let be the number of matrices in with height bounded by . We determine the asymptotic behaviour of as goes to infinity including an error term,with being the degree of . The constant involves the discriminant of , an integral depending only on the signature of , and the value of the Dedekind zeta function...
Counting irreducible polynomials over finite fields
In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: where denotes the number of monic irreducible polynomials in with norm .