Interpolation Determinants
After the myriad of successes gleaned from using existent but not explicit auxiliary functions, in the 1990s Michel Laurent introduced the idea of interpolation determinants. These are alternants – determinants of matrices of the form
where φi are a set of functions interpolated at a set of points ζj. Since a determinant is just a polynomial in the entries of a matrix, these auxiliary functions succumb to study by analytic means. A problem with the method was the need to choose a basis before the matrix could be worked with. A development by Jean-Benoît Bost removed this problem with the use of Arakelov theory, and research in this area is ongoing. The example below gives an idea of the flavour of this approach.
Read more about this topic: Auxiliary Function