??so ... ?? are we claiming that all cube roots of integers are rationally definable in terms of equal-division points of the eisenstein elliptic curve, and all 4th roots in terms of equal-division points of the lemniscate ??? .... ???? ....

??relationship to way ... lemniscate traditionally presented in terms of quartic ... ???? ...... ?? maybe also eisenstein in terms of cubic ??? .... ????? .....


?? all square roots in terms of equal-division points of gl(1) ... ??? ....

?? that bit about ... ??? "solving arbitrary polynomial equation in one variable in terms of modular functions" ... ???? .... ???? .....

?? dimensional algebra of modular forms ... vs dimensional algebra of fractional ideals ... ?? ....

?? "alternation between randomness and order" ... ???? ....

?? diamond and shurman ... preface ... analogy ... ??? .... ??? can i find some of my notes on that stuff ... trying to figure out what they were really saying ... system of eigenvalues ..... ???? .... ???? .....

?? cubic reciprocity and ... ???... maybe obtaining cube root of n from nth equal-division points of eisenstein curve ??? ... ?? and similarly for biquadratic reciprocity ??? ....

?? cubic (?? ...) numbers obtainable from nth equal-division points of gl(1) ... ??? ....

??vague memories of something ... ?? maybe vaguely like one of above ... ??? ...