Hiroshima Mathematical Journal

A family of entire functions which determines the splitting behavior of polynomials at primes

Hajime Kuroiwa

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Abstract

In this paper, we prove that there exist entire functions which determines the splitting behavior of polynomials at prime. 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.

Article information

Source
Hiroshima Math. J., Volume 41, Number 3 (2011), 409-411.

Dates
First available in Project Euclid: 12 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1323700042

Digital Object Identifier
doi:10.32917/hmj/1323700042

Mathematical Reviews number (MathSciNet)
MR2895288

Zentralblatt MATH identifier
1238.11034

Subjects
Primary: 11A41: Primes 11A51: Factorization; primality

Keywords
Entire function completely splitting non-abelian class field theory

Citation

Kuroiwa, Hajime. A family of entire functions which determines the splitting behavior of polynomials at primes. Hiroshima Math. J. 41 (2011), no. 3, 409--411. doi:10.32917/hmj/1323700042. https://projecteuclid.org/euclid.hmj/1323700042


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References

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