Speaker
Description
We will discuss universal algebraic functions, i.e., polynomial equations (or systems of such equations) with independent variable coefficients. It is known that for such equations the algebraic functions have hypergeometric type (Mellin 1921, Birkeland 1927, Stepanenko 2015).
For functions of hypergeometric type, we prove an anlogue of Gorn-Kapranov theorem (1889-1991) that states that the singularities of such functions coincide with the discriminant sets of the corresponding systems. The results obtained make it possible to calculate the convergence domains for series of hypergeometric type in the language of functional inequalities for modules of variables of power series. Existence of such inequalities can be interpreted as an appearance of "quantum entanglement" in the theory of hypergeometric structures of Feynman integrals.
