Examples with "theta function" and their translation in Chinees
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He discovered many of the fundamental properties of theta functions, including the functional equation and the Jacobi triple product formula, as well as many other results on q-series and hypergeometric series.
The letters he exchanged with Jacobi show that Hermite had discovered some differential equations satisfied by theta-functions and he was using Fourier series to study them. He had found general solutions to the equations in terms of theta-functions.
In 1929 Coble published the monograph Algebraic geometry and theta functions in the American Mathematical Society Colloquium Publications, being the tenth such volume.
He wrote the important Abel's Theorem and the Allied Theory of Theta Functions in 1897 and another major contribution Multiply Periodic Functions in 1907.
Essentially new points of view... particularly concerning the transformation theory of theta-functions... were introduced by Eisenstein in the fundamental but seldom quoted "Beiträge zur Theorie der elliptischen Funktionen" published in Crelle's Journal in 1847, which are based upon entirely original ideas...
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