The Weierstrass \wp-function of the hexagonal lattice

2021/05/10 by Vassilis G. Papanicolaou, Papanicolaou, Vassilis G.
Chemistry · Mathematics · #14H52 #30C15 #30D05 #30D99 #Characterization (materials science) #Chemistry #Combinatorics #Complex Variables (math.CV) #Condensed matter physics #Crystallography #FOS: Mathematics #Function (biology) #Hexagonal crystal system #Hexagonal lattice #Holomorphic and Operator Theory #Lattice (music) #Mathematical functions and polynomials #Mathematics #Meromorphic and Entire Functions #Meromorphic function #Optics #Physics #Primary: 33E05. Secondary: 11D25 #Pure mathematics #Weierstrass functions #math.CV #msc:11D25 #msc:14H52 #msc:30C15 #msc:30D05 #msc:30D99 #msc:33E05.

paper · pdf · doi:10.48550/arxiv.2105.04307

published in arXiv (Cornell University) (Cornell University) · 11 pages

arxiv created 2021/05/10 · openalex publication_date 2021/05/10 · arxiv updated 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We present some properties of the Weierstrass \wp-function associated to the hexagonal (or triangular) lattice. In particular, with the help of an old theorem of I.N. Baker \citeB on the characterization of meromorphic solutions of the equation X³ + Y³ = 1 we determine the zeros of the function \wp'(z) ± √(3).

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