Abstract
Automorphic forms, encompassing modular forms and Maass forms, are completely described by their Fourier coefficients and/or Laplace eigenvalues. We present efficient methods for computing the Fourier coefficients of modular forms of any weight, and certifying the Laplace eigenvalues of Maass forms of weight 0.In all cases, the methods presented are applicable to forms of arbitrary level and character. In the case of modular forms, the value of our work is from efficiency improvements over pre-existing methods, which we demonstrate with several examples of practical applications. In the case of Maass forms, our work represents the first known method for certifying these forms, and we subsequently apply our method to produce the first known certified Maass form with non-trivial character.
| Date of Award | 6 Dec 2022 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | M Lee (Supervisor), Andrew R Booker (Supervisor) & Joseph Najnudel (Supervisor) |