A family of entire functions which determines the splitting behavior of polynomials at primes. (English) Zbl 1238.11034

Author’s abstract: We prove that there exist entire functions which determine the splitting behavior of polynomials at primes. First, to any monic irreducible polynomial and any prime \(p\), we associate a function defined on the set of primes which determines whether the polynomial splits completely at \(p\) or not. Then we extend them to entire functions.


11C08 Polynomials in number theory
30D99 Entire and meromorphic functions of one complex variable, and related topics
11R09 Polynomials (irreducibility, etc.)
Full Text: Euclid


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