|
In mathematics, a theta constant or Thetanullwert (German for theta zero value; plural Thetanullwerte) is the restriction ''θ''''m''(''τ'') = θ''m''(''τ'',''0'') of a theta function ''θ''''m''(τ,''z'') with rational characteristic ''m'' to ''z'' = 0. The variable ''τ'' may be a complex number in the upper half-plane in which case the theta constants are modular forms, or more generally may be an element of a Siegel upper half plane in which case the theta constants are Siegel modular forms. The theta function of a lattice is essentially a special case of a theta constant. ==Definition== The theta function ''θ''''m''(''τ'',''z'') = ''θ''''a'',''b''(''τ'',''z'')is defined by : where * ''n'' is a positive integer, called the genus or rank. * ''m'' = (''a'',''b'') is called the characteristic * ''a'',''b'' are in R''n'' * ''τ'' is a complex ''n'' by ''n'' matrix with positive definite imaginary part * ''z'' is in C''n'' * ''t'' means the transpose of a row vector. If ''a'',''b'' are in Q''n'' then ''θ''''a'',''b''(''τ'',0) is called a theta constant. 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「Theta constant」の詳細全文を読む スポンサード リンク
|