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In mathematics, a fundamental pair of periods is an ordered pair of complex numbers that define a lattice in the complex plane. This type of lattice is the underlying object with which elliptic functions and modular forms are defined. Although the concept of a two-dimensional lattice is quite simple, there is a considerable amount of specialized notation and language concerning the lattice that occurs in mathematical literature. This article attempts to review this notation, as well as to present some theorems that are specific to the two-dimensional case. ==Definition== The fundamental pair of periods is a pair of complex numbers such that their ratio ω2/ω1 is not real. In other words, considered as vectors in , the two are not collinear. The lattice generated by ω1 and ω2 is : This lattice is also sometimes denoted as Λ(ω1, ω2) to make clear that it depends on ω1 and ω2. It is also sometimes denoted by Ω or Ω(ω1, ω2), or simply by 〈ω1, ω2〉. The two generators ω1 and ω2 are called the lattice basis. The parallelogram defined by the vertices 0, and is called the fundamental parallelogram. It is important to note that, while a fundamental pair generates a lattice, a lattice does not have any unique fundamental pair, that is, many (in fact, an infinite number) fundamental pairs correspond to the same lattice. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「fundamental pair of periods」の詳細全文を読む スポンサード リンク
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