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PreprintCC BY-ND 4.0HAL

A NOTE ON THE RAMIFICATION CHARACTER, RAMIFICATION POLYNOMIALS AND ASSOCIATED DIRICHLET L-FUNCTION

  • Theophilus Agama
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Abstract

In this paper, we introduce and study special types of polynomials whose coefficients are determined by the ramification characters κm(·) in a fixed modulo m≥ 2. These characters serve as indicator functions for integers that admit a binary representation where a summand is generated from the residue class of a modulus of lower magnitude by a given positive integer. We derive analytical properties for these polynomials investigating the Dirichlet L-function L(s,κm(·)):=∑ n=1∞κm(n)/ns associated with the ramification character.

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Cite

BibTeXRIS
BibTeX
@misc{agama2026note,
  title = {{A NOTE ON THE RAMIFICATION CHARACTER, RAMIFICATION POLYNOMIALS AND ASSOCIATED DIRICHLET L-FUNCTION}},
  author = {Theophilus Agama},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05838145v1},
  note = {CC BY-ND 4.0},
}
RIS
TY  - UNPB
TI  - A NOTE ON THE RAMIFICATION CHARACTER, RAMIFICATION POLYNOMIALS AND ASSOCIATED DIRICHLET L-FUNCTION
AU  - Theophilus Agama
PY  - 2026
DA  - 2026/10/24
PB  - HAL
UR  - https://hal.science/hal-05838145v1
AB  - In this paper, we introduce and study special types of polynomials whose coefficients are determined by the ramification characters κ_m(·) in a fixed modulo m≥ 2. These characters serve as indicator functions for integers that admit a binary representation where a summand is generated from the residue class of a modulus of lower magnitude by a given positive integer. We derive analytical properties for these polynomials investigating the Dirichlet L-function L(s,κ_m(·)):=∑ _n=1^∞κ_m(n)/n^s associated with the ramification character.
ER  -