Abel's Theorem and the Allied Theory: Including the Theory of the Theta Functions |
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Common terms and phrases
a₁ Abel's theorem adjoint polynomial algebraic arbitrary constants arbitrary place B₁ b₂ branch places C₂ Chap chapter condition coresidual corresponding Crelle denote determinant dimension double points elements equal equation essential singularities exist expression factor finite places formula function of order fundamental G₁ given Göpel system h₁ half-integer half-integer characteristics half-periods Hence hyperelliptic infinite infinitesimal infinity integers integral function integral polynomial intersections k₁ linear linear transformation linearly independent m₁ Math matrix obtain p-polynomial vanishing P₁ period loops places c₁ plane curve poles polynomial of grade prove quantities quartic rational function result Riemann surface satisfied second kind second order shew shewn suppose theorem theory theta functions transformation U₁ values variable w₁ Weierstrass's wherein x₁ y₁ zero α₁
Popular passages
Page 314 - 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.