39 citations · 144 across the 16 of their papers we have counts for
8 papers · 1 filter
P-adic approximation of algebraic integers and residue class rings of rings of integer-valued polynomials
Sophie Frisch, Franz Halter-Koch
Let F:K be a Galois extension of number fields and Q a prime ideal of O_F lying over the prime P of O_K. By analyzing the Q-adic closure of O_K in O_F we characterize those rings o…
Integer-valued polynomials on discrete valuation rings of global fields with prescribed lengths of factorizations
Victor Fadinger, Sophie Frisch, Daniel Windisch
Let be a valuation ring of a global field . We show that for all positive integers and there exists an integer-valued polynomial on , t…
Relative polynomial closure and monadically Krull monoids of integer-valued polynomials
Sophie Frisch
Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f in Int(D), we explicitly construct a divisor homomorphism from [f], the divisor-closed sub…
Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples
Sophie Frisch, Leonid Vaserstein
A Pythagorean n-tuple is an integer solution of x_1^2+...+x_{n-1}^2=x_n^2. For n=4 and n=6, the Pythagorean n-tuples admit a parametrization by a single n-tuple of polynomials with…
Non-unique factorization of polynomials over residue class rings of the integers
Christopher Frei, Sophie Frisch
We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] i…
Polynomial parametrization of the solutions of Diophantine equations of genus 0
Sophie Frisch, Günter Lettl
Let f in Z[X,Y,Z] be a non-constant, absolutely irreducible, homogeneous polynomial with integer coefficients, such that the projective curve given by f=0 has a function field isom…
Remarks on polynomial parametrization of sets of integer points
Sophie Frisch
If, for a subset S of Z^k, we compare the conditions of being parametrizable (a) by a single k-tuple of polynomials with integer coefficients, (b) by a single k-tuple of integer-va…
Parametrization of Pythagorean triples by a single triple of polynomials
Sophie Frisch, Leonid Vaserstein
It is well known that Pythagorean triples can be parametrized by two triples of polynomials with integer coefficients. We show that no single triple of polynomials with integer coe…