A Remark on the Nevanlinna-Pólya Theorem in Analytic Function Theory

On the Pólya Enumeration Theorem

Simple formulas for the number of different cyclic and dihedral necklaces containing nj beads of the j-th color, j ≤ m and ∑m j=1 nj = N , are derived. Among a vast number of counting problems one of the most popular is a necklace enumeration. A cyclic necklace is a coloring in m colors of the vertices of a regular N–gon, where two colorings are equivalent if one can be obtained from the other ...

Nevanlinna on Analytic Functions

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

The Nevanlinna Theorem of the Classical Theory of Moments Revisited

The canonical solutions of the truncated Hamburger moment problem (both in the classical and degenerate cases) are found. The Nevanlinna theorem which provides the noncanonical solutions of the truncated Hamburger problem is also rederived in the framework of the operator approach.

A Remark on Zoloterav’s Theorem

Let n ≥ 3 be an odd integer. For any integer a prime to n, define the permutation γ a,n of {1,. .. , (n − 1)/2} by γ a,n (x) = n − {ax} n if {ax} n ≥ (n + 1)/2, {ax} n if {ax} n ≤ (n − 1)/2, where {x} n denotes the least nonnegative residue of x modulo n. In this note, we show that the sign of γ a,n coincides with the Jacobi symbol a n if n ≡ 1 (mod 4), and 1 if n ≡ 3 (mod 4).