Mathematics, Department of


Date of this Version



Published in Bull. Amer. Math. Soc. 38 (1932) 560-568. Used by permission.


The class of meromorphic functions which satisfy periodicity relations of the form (1) ƒ(z + 2ωl) = c1f(z), f(z + 2ω2) = c2f{z), where the multipliers c1 and c2 are independent of z, and ωl2 is a complex number with non-vanishing imaginary part, has been named by Hermite doubly periodic of the second kind. It is possible to make the study of these functions depend on others of the same type, but such that one of the multipliers, say cl, is unity. In what follows we shall assume, further, that the periods (2ωl, 2ω2) are (π, πτ), where τ = a +ib, b>0.

Included in

Mathematics Commons