"The Weierstrass zeta function was called an integral of the second kind in elliptic function theory; it is a logarithmic derivative of a theta function, and therefore has simple poles, with integer residues."

?? "logarithmic derivative" and "mellin transform" ???? ..... not clear from google hits ...


"The decomposition of a (meromorphic) elliptic function into pieces of 'three kinds' parallels the representation as (i) a constant, plus (ii) a linear combination of translates of the Weierstrass zeta function, plus (iii) a function with arbitrary poles but no residues at them.

The same type of decomposition exists in general, mutatis mutandis, though the terminology is not completely consistent. In the algebraic group (generalized Jacobian) theory the three kinds are abelian varieties, algebraic tori, and affine spaces, and the decomposition is in terms of a composition series."

hmmmm... ??? ....


"The dimension of the space of differentials of the first kind, by means of this identification, is the Hodge number h^[0,1]."

??? .....