Kategorie: AG Algebra, Geometrie und Computeralgebra
By adding certain equianharmonic elliptic sigma functions to the
coefficients of the Borwein cubic theta functions, an interesting set of six
two-variable theta functions may be derived. These theta functions
invert a special case of Appell’s hypergeometric function and
satisfy several identities akin to those satisfied by the Borwein
cubic theta functions. In this talk I will discuss the modular
properties of these functions as well as the computation of their
modular equations, which turn out to be algebraic surfaces. An
application of these results is a new two-parameter family X^9 −
3*X^8 + 4*t*X^6 − 6*s*X^5 − 6*s*X^4 + 4*s*t*X^3 − 3*s^2*X + s^2 = 0
of solvable nonic equations.
