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Theta series and weight enumerator over an imaginary quadratic field

Ankur

Department of Mathematics, VIT-AP University, Amaravati 522237, India

E-mail Address: ankur.singh@vitap.ac.in

Corresponding author.

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and

K. P. Shum

Institute of Mathematics, Yunnan University, Kunming, P. R. China

E-mail Address: kpshum@ynu.edu.cn

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https://doi.org/10.1142/S1793557121500984Cited by:0 (Source: Crossref)

Abstract

In this paper, we consider an imaginary quadratic field $K = ℚ (\sqrt{- m})$ with $- m \equiv 3$ (mod $4$ ). In particular, we study the ring of integers corresponding to the field $K$ and visualize the form of $𝜖_{K} / p 𝜖_{K}$ . We also consider lattices over the ring of integers $𝜖_{K}$ and discuss the theta series to see its relation with the weight enumerator. As a consequence, we will see how the theta series differs for different $m$ and $m^{'}$ .

Communicated by B. K. Dass

Keywords:

AMSC: 06D50, 94B05, 11F27

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