Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart. In the physical world, objects often push each other apart in an ...

Abstract. Given a separable nonconstant polynomial f(x) with integer coefficients, we consider the set S consisting of the squarefree parts of all the rational values of f(x), and study its behavior ...

A mathematician has uncovered a way of answering some of algebra's oldest problems. University of New South Wales Honorary Professor Norman Wildberger, has revealed a potentially game-changing ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

It is known that the expected number of zeros in the interval (-1, 1) of the sum a0ψ0(t) + a1ψ1(t) + ⋯ + anψn(t), in which ψk(t) is the normalized Legendre polynomial of degree k and the coefficients ...