Modular eigenforms at the boundary of weight space

  • Jan VonkEmail author


Andreatta, Iovita, and Pilloni recently introduced \({{\mathrm{\mathbf {F}}}}_p(({{\mathrm{\mathrm {t}}}}))\)-Banach spaces of overconvergent \({{\mathrm{\mathrm {t}}}}\)-adic modular forms, whose weight may be considered a “boundary” point of weight space. In an effort to make them concrete and accessible to explicit experimentation, we construct orthonormal bases, deduce \({{\mathrm{\mathrm {t}}}}\)-adic analogues of certain p-adic results in the literature, and exhibit explicit examples.


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBurnside HallMontrealCanada

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