Open AccessOn the representation of the Picard modular function by $θ$ constants I-II
Author(s) -
Hironori Shiga
Publication year - 1988
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195175031
Subject(s) - mathematics , modular form , modular design , modular curve , function (biology) , pure mathematics , constant (computer programming) , algebraic number , algebra over a field , representation (politics) , domain (mathematical analysis) , combinatorics , discrete mathematics , mathematical analysis , computer science , programming language , evolutionary biology , politics , political science , law , biology
In this paper the author shows the representation of the Picard modular function by 0 constants, and characterizes this function as modular forms on the domain D= {(M, z;) eC : 2Re v + \u <0} = relative to a certain arithmetic discontinuous group, " 0 1 0 where H= 1 0 0 . 0 0 1 We divide the paper in two parts. In Part I we discuss the former subject and in Part II we study the latter. This modular function was constructed originally by [P], and was investigated by several mathematicians recently [D-M], [F], [H], [Sh] and [T]. This modular function is defined as the inverse mapping of the period mapping 0 for the family of the complex algebraic curves in (z,w) -space
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom