14:00 - 15:00, November 13, 2025 (Thursday) Room 515, Cosmology Building, NTU
(臺灣大學次震宇宙館 515研討室)
On Some Inadmissible Values of the Fourier Coefficients of Special Newforms with Level 1 or 2 Akihiro Goto (Kyushu University)
Abstract
In 1947, Lehmer conjectured that Ramanujan's -function never vanishes, where the function is defined as the Fourier coefficient of the newform of weight 12 and level 1. This conjecture is still open. It is natural to consider whether any given integer belongs to the image of the -function. Recently, it is proved that , , are not -values, where < 100 is an odd prime, by Balakrishnan, Ono, Craig and many other people. The speaker would like to talk about that , , , and are not -values, except for a few cases, where is an odd prime. I would also like to present similar results obtained for the newform of weight 8 and level 2.
