| 21. | The theta function of a lattice is then a holomorphic function on the upper half-plane.
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| 22. | One of the major achievements of Bernhard Riemann was his theory of complex tori and theta functions.
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| 23. | This was also a beginning of a substantial development by others, connecting representation theory and theta functions.
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| 24. | These formulas can, therefore, be used to define the Theta functions over other-adic numbers.
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| 25. | In the analytic theory, there are four fundamental theta functions in the theory of Jacobian elliptic functions.
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| 26. | This is applied in the theory of theta functions, and is a possible method in geometry of numbers.
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| 27. | The next simplest cases of a disc or square involve, respectively, Bessel functions and Jacobi theta functions.
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| 28. | The holomorphic parts of certain weak Maass wave forms turn out to be essentially Ramanujan's mock theta functions.
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| 29. | The theta function of a unimodular positive definite lattice is a modular form whose weight is one half the rank.
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| 30. | He worked with ideas related to those of Weierstrass, Riemann and Heinrich Weber on theta functions and Gaussian sums.
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