12 citations · 27 across the 11 of their papers we have counts for
15 papers
Algebraic and analytic structure of Morikawa's sangaku problem
David Krumm
Let denote the minimal side length of a square inscribed in the curvilinear triangular region formed by two tangent circles of radii and together with their co…
A Course in Ring Theory
David Krumm
This book is a rigorous and conceptually oriented introduction to ring theory. The emphasis is on structural understanding rather than encyclopedic coverage: rings are studied thro…
Dynatomic Galois groups for a family of quadratic rational maps
David Krumm, Allan Lacy
For every nonconstant rational function , the Galois groups of the dynatomic polynomials of encode various properties of that are of interest in the subj…
Quadratic points on dynamical modular curves
John R. Doyle, David Krumm
Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This yields a classification statem…
Morikawa's Unsolved Problem
Jan E. Holly, David Krumm
By combining theoretical and computational techniques from geometry, calculus, group theory, and Galois theory, we prove the nonexistence of a closed-form algebraic solution to a J…
Twists of hyperelliptic curves by integers in progressions modulo
David Krumm, Paul Pollack
Let be a nonconstant polynomial with integer coefficients and nonzero discriminant. We study the distribution modulo primes of the set of squarefree integers such that t…
A finiteness theorem for specializations of dynatomic polynomials
David Krumm
Let and be indeterminates, let , and for every positive integer let denote the dynatomic polynomial of . Let…
Galois groups over rational function fields and explicit Hilbert irreducibility
David Krumm, Nicole Sutherland
Let be a polynomial in two variables with rational coefficients, and let be the Galois group of over the field . It follows from Hilbert'…
Galois groups in a family of dynatomic polynomials
David Krumm
For every nonconstant polynomial , let denote the fourth dynatomic polynomial of . We determine here the structure of the Galois group and the degree…
Explicit Hilbert Irreducibility
David Krumm
Let be an irreducible polynomial in two variables with rational coefficients. It follows from Hilbert's Irreducibility Theorem that for most rational numbers the speci…
A local-global principle in the dynamics of quadratic polynomials
David Krumm
Let be a number field, a quadratic polynomial, and . We show that if has a point of period in every non-archimedean completion of , then $…
Squarefree parts of polynomial values
David Krumm
Given a separable nonconstant polynomial with integer coefficients, we consider the set consisting of the squarefree parts of all the rational values of , and stud…
Computing points of bounded height in projective space over a number field
David Krumm
We construct an algorithm for solving the following problem: given a number field , a positive integer , and a positive real number , determine all points in $\mathbb P^N(…
Preperiodic points for quadratic polynomials over quadratic fields
John R. Doyle, Xander Faber, David Krumm
To each quadratic number field and each quadratic polynomial with -coefficients, one can associate a finite directed graph whose vertices are the -rational p…
Computing algebraic numbers of bounded height
John R. Doyle, David Krumm
We describe an algorithm for listing all elements of bounded height in a given number field.