Generating weights for the Weil representation attached to an even order cyclic quadratic module
| Autor: | Luca Candelori, Gene S. Kopp, Cameron Franc |
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| Rok vydání: | 2017 |
| Předmět: |
Complex representation
quadratic module Modular form metaplectic group Theta function 0102 computer and information sciences critical weights 01 natural sciences Prime (order theory) Combinatorics Quadratic equation vector-valued modular form theta function FOS: Mathematics Order (group theory) Number Theory (math.NT) 0101 mathematics half-integral weight Mathematics imaginary quadratic field Algebra and Number Theory Mathematics - Number Theory 010102 general mathematics Dirichlet class number formula Weil representation quadratic form generating weights Algebra Metaplectic group 010201 computation theory & mathematics Quadratic form metaplectic orbifold Serre duality positive-definite lattice |
| Zdroj: | Candelori, L, Franc, C & Kopp, G 2017, ' Generating weights for the Weil representation attached to an even order cyclic quadratic module ', Journal of Number Theory, vol. 180, pp. 474-497 . https://doi.org/10.1016/j.jnt.2017.04.017 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2017.04.017 |
| Popis: | Text We develop geometric methods to study the generating weights of free modules of vector-valued modular forms of half-integral weight, taking values in a complex representation of the metaplectic group. We then compute the generating weights for modular forms taking values in the Weil representation attached to cyclic quadratic modules of order 2 p r , where p ≥ 5 is a prime. We also show that the generating weights approach a simple limiting distribution as p grows, or as r grows and p remains fixed. Video For a video summary of this paper, please visit https://youtu.be/QNbPSXXKot4 . |
| Databáze: | OpenAIRE |
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