2025/09/25 by Kurt Girstmair, Girstmair, Kurt
Computer Science · Mathematics · #Digital Filter Design and Implementation #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.2509.21094
openalex publication_date 2025/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a survey of a connection between the distribution of certain power residues modulo p, p a prime, and relative class numbers. The focus lies on quadratic residues and sixth power residues. Dirichlet's class number formula yields a number of results about the distribution of quadratic residues, for instance, the well-known fact that the interval [0,p/2] contains more quadratic residues than nonresidues. This class number formula is also responsible for some properties of the digit expansions of numbers m/p, p\NDIV m. In a certain sense the results based on Dirichlet's formula can be extended to sixth power residues, where geometry plays an important role.