Theta Functions with Harmonic Coefficients over Number Fields |
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| Authors: | Olav K Richter |
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| Institution: | Department of Mathematics, University of California at Santa Cruz, Santa Cruz, California, 95064, Department of Mathematics, University of North Texas, Denton, Texas, 76203, f1richter@math.ucsc.eduf1, f2richter@unt.eduf2 |
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| Abstract: | We investigate theta functions attached to quadratic forms over a number field K. We establish a functional equation by regarding the theta functions as specializations of symplectic theta functions. By applying a differential operator to the functional equation, we show how theta functions with harmonic coefficients over K behave under modular transformations. |
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