CachedQFunctions(C, L)ΒΆ

cachedqfunct.spad line 90 [edit on github]

CachedQFunctions implements a cache for powers of functions from QFunctions.

eulerFunctionPower: (PositiveInteger, Integer) -> L

eulerFunctionPower(n, e) computes (prod_{k=1}^infty(1-q^{kn}))^e.

jacobiFunctionPower: (PositiveInteger, PositiveInteger, Integer) -> L

jacobiFunctionPower(d,g,e) computes and caches jacobiFunction(d,g)^e from QFunctions(C,L).

kleinJInvariantPower: (PositiveInteger, Integer) -> L

kleinJInvariantPower(d,e) computes and caches multiplyExponents((kleinJInvariant()$QFunctions(C,L))^e,d).

modularLambdaPower: (PositiveInteger, Integer) -> L

modularLambdaPower(n, e) computes the q-series (q=exp(pi*i*tau)) of $lambda(n tau)^e$. The modular lambda function is defined by $lambda(tau)=theta_2(0,q)^4/theta_3(0,q)^4$. See https://en.wikipedia.org/wiki/Modular_lambda_function https://fungrim.org/topic/Modular_lambda_function/

thetaPower4: PositiveInteger -> L

The function thetaPower4(j) returns $theta_j(0,q)^4$ for j=2,3,4, i.e. the 4th power of the theta constants.