ICTS:31869

Video URL

The p-adic constant for mock modular forms associated to CM forms

The p-adic constant for mock modular forms associated to CM forms

(2025). The p-adic constant for mock modular forms associated to CM forms. SciVideos. https://youtube.com/live/zHuBcISLeFU

The p-adic constant for mock modular forms associated to CM forms. SciVideos, May. 26, 2025, https://youtube.com/live/zHuBcISLeFU 

          @misc{ scivideos_ICTS:31869,
            doi = {},
            url = {https://youtube.com/live/zHuBcISLeFU},
            author = {},
            keywords = {},
            language = {en},
            title = {The p-adic constant for mock modular forms associated to CM forms},
            publisher = {},
            year = {2025},
            month = {may},
            note = {ICTS:31869 see, \url{https://scivideos.org/icts-tifr/31869}}
          }
Ryota Tajima
Talk numberICTS:31869
Source RepositoryICTS-TIFR

Abstract

For a normalized newform g in S_{k}(\Gamma_{0}(N)) with complex multiplication by an imaginary quadratic field K, there is a mock modular form f^{+} corresponding to g. K. Bringmann, P. Guerzhoy, and B. Kane modified f^{+} to obtain the p-adic modular form by a certain p-adic constant \alpha_{g}. In addition, they showed that \alpha_{g}=0 if p is split in K and does not divide N. On the other hand, the speaker showed that \alpha_{g} is a p-adic unit for an inert prime p that does not divide 2N when \dim S_{k}(\Gamma_{0}(N))=1. In this talk, the speaker determines the p-adic valuation of \alpha_{g} for an inert prime p under a mild condition, when g has weight 2 and rational Fourier coefficients.