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Showing 1 to 3 of 3 for “"Reciprocity theorems"”.
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Contributions to Trigonometric Sums and Fifth -Order Mock Theta Functions
… also a survey on the history of evaluations and reciprocity theorems on such sums. We establish some general theorems on explicit evaluations and reciprocity theorems using contour integration as our main method. The second portion of this thesis focuses on Ramanujan's mock theta functions. In …
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Product Identities for Theta Functions
… 3, we give a proof of a generalized form of a reciprocity theorem in Ramanujan's lost notebook. Also we generalize the results obtained by S.-Y. Kang in [38]. Then several new reciprocity theorems and their applications are presented. In Chapter 4, we prove the Jacobi triple product identity, …
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Quadratic and cubic reciprocity
… seek to prove results about quadratic and cubic reciprocity in great detail. Although these results appear in many textbooks, the proofs often contain large gaps that may be difficult for the average reader to follow. To achieve this goal, we have 'built up to reciprocity theory from basic …