## Abel's Theorem and the Allied Theory: Including the Theory of the Theta Functions |

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Abel's theorem adjoint polynomial algebraic arbitrary constants arbitrary place argument branch places Chap chapter characteristics condition considered coresidual corresponding Crelle cubic surface denote determined differential coefficients dimension double points equal essential singularities exist expression factor factorial function finite places follows formula function of order fundamental equation given half-integer half-period Hence hyperelliptic hyperelliptic surface infinite infinitesimal infinity integral function integral polynomial intersections linear aggregates linearly independent Math matrix multiple neighbourhood Noether notation number of zeros obtain period loops plane curve poles polynomial of grade polynomial vanishing positive integer prove Q places quantities quartic rational function regard result Riemann surface Riemann-Roch Theorem right hand satisfied second kind second order sheets shew shewn suppose symmetrical matrix tangents theorem theta functions third kind transformation values vanish identically variable Weierstrass's wherein

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Page 368 - T) denote the excess of the number of zeros over the number of poles in the part of the rectangle for which a > a , zeros or poles on t = 0 or t = T counting one-half only.