Abel's theorem and the allied theory, including the theory of the theta functions (1897)
Baker, H. F. (Henry Frederick), 1866-1956 · Cambridge : University Press · leaf 594
uation associated withthe hyperelliptic case y^ = ^ {x — c^) {x — ai) {x — C2) {x — a^)...{x - Cp) {x — ap){x — c), be real and in ascending order of magnitude, we may usefully modify thenotation of § 200, Chap. XI. Denote these roots, in order, by h,p, 6^p_,, ...,ho, 342] TO THE HYPERELLIPTIC… … Fig. 17. Then if U^, ..., U^ are linearly independent integrals of the first kind,such that dUldx = <^rly, where i/r,. is an integral polynomial in x, of degreep — 1 at most, with only real coefficients, the half-periods are respectively real and purely imaginary, so that [&),■, i] is also…
Geometry, Algebraic · Functions, Theta
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