TY - JOUR
T1 - On Eisenstein polynomials and zeta polynomials II
AU - Miezaki, Tsuyoshi
AU - Oura, Manabu
N1 - Funding Information:
The authors thank Koji Chinen and Iwan Duursma for their helpful discussions and contributions to this research. The authors would also like to thank the anonymous reviewers for their beneficial comments on an earlier version of the manuscript. The authors are supported by JSPS KAKENHI (18K03217,17K05164).
Publisher Copyright:
© 2020 World Scientific Publishing Company.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - Eisenstein polynomials, which were defined by the second author, are analogues to the concept of an Eisenstein series. The second author conjectured that there exist some analogous properties between Eisenstein series and Eisenstein polynomials. In the previous paper, the first author provided new analogous properties of Eisenstein polynomials and zeta polynomials for the Type II case. In this paper, the analogous properties of Eisenstein polynomials and zeta polynomials are shown to also hold for the Type I, Type III, and Type IV cases. These properties are finite analogies of certain properties of Eisenstein series.
AB - Eisenstein polynomials, which were defined by the second author, are analogues to the concept of an Eisenstein series. The second author conjectured that there exist some analogous properties between Eisenstein series and Eisenstein polynomials. In the previous paper, the first author provided new analogous properties of Eisenstein polynomials and zeta polynomials for the Type II case. In this paper, the analogous properties of Eisenstein polynomials and zeta polynomials are shown to also hold for the Type I, Type III, and Type IV cases. These properties are finite analogies of certain properties of Eisenstein series.
KW - Eisenstein polynomials
KW - weight enumerators
KW - zeta polynomials
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U2 - 10.1142/S1793042120500116
DO - 10.1142/S1793042120500116
M3 - Article
AN - SCOPUS:85072510335
SN - 1793-0421
VL - 16
SP - 207
EP - 218
JO - International Journal of Number Theory
JF - International Journal of Number Theory
IS - 1
ER -