On places of algebraic function fields.
On polynomial transformations in several variables
On polynomials taking small values at integral arguments
On power integral bases for certain pure number fields defined by
Let be a number field generated by a complex root of a monic irreducible polynomial , , is a square free rational integer. We prove that if or and , then the number field is monogenic. If or , then the number field is not monogenic.
On power residue characters of units and the representation of numbers by quadratic forms
On power residues
On power residues
On power series with only finitely many coefficients(mod 1): Solution of a problem of Pisot and Salem
On q-orders in primitive modular groups
We prove an upper bound for the number of primes p ≤ x in an arithmetic progression 1 (mod Q) that are exceptional in the sense that has no generator in the interval [1,B]. As a consequence we prove that if with a sufficiently large absolute constant c, then there exists a prime q dividing Q such that for some positive integer b ≤ B. Moreover we estimate the number of such q’s under suitable conditions.
On Quadratic forms isotropic over the function field of a comic.
On R. Chapman's "evil determinant": case p ≡ 1 (mod 4)
For p ≡ 1 (mod 4), we prove the formula (conjectured by R. Chapman) for the determinant of the (p+1)/2 × (p+1)/2 matrix with .
On Ray Class Annihilators of Cyclotomic Fields.
On ray class annihilators of cyclotomic function fields
On real quadratic number fields suitable for cryptography.
On reciprocity equivalence of quadratic number fields
On Rédei's theory of the Pell equation.
On relations between units of normal algebraic number fields and their subfields
On relative integral bases for unramified extensions
0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely generated and...
On relative pure cyclic fields with power integral bases
Let be an extension of a number field , where satisfies the monic irreducible polynomial of prime degree belonging to ( is the ring of integers of ). The purpose of this paper is to study the monogenity of over by a simple and practical version of Dedekind’s criterion characterizing the existence of power integral bases over an arbitrary Dedekind ring by using the Gauss valuation and the index ideal. As an illustration, we determine an integral basis of a pure nonic field with a...
On representation of cyclotomic fields