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 ...

Description: An introduction to Galois theory, covering both its origins in the theory of roots of polynomial equations and its modern formulation in terms of abstract algebra. Topics include finite ...

A new method for interpolation by rational functions of prescribed numerator and denominator degrees is presented. When the interpolation nodes are roots of unity or Chebyshev points, the algorithm is ...

If f is a nonzero complex-valued function defined on a finite abelian group A and f̂ is its Fourier transform, then |supp(f)|| supp(f̂)| ≥ |A|, where supp(f) and supp(f̂) are the supports of f and f̂.