抄録
In 1947, Lehmer conjectured that the Ramanujan τ-function τ(m) is non-vanishing for all positive integers m, where τ(m) are the Fourier coefficients of the cusp form δ of weight 12. It is known that Lehmer's conjecture can be reformulated in terms of spherical t-design, by the result of Venkov. In this paper, we show that τ(m) = 0 is equivalent to the fact that the homogeneous space of the moonshine vertex operator algebra (V{music natural sign})m+1 is a conformal 12-design. Therefore, Lehmer's conjecture is now reformulated in terms of conformal t-designs.
本文言語 | English |
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ページ(範囲) | 59-65 |
ページ数 | 7 |
ジャーナル | Journal of Algebra |
巻 | 374 |
DOI | |
出版ステータス | Published - 2013 1月 15 |
外部発表 | はい |
ASJC Scopus subject areas
- 代数と数論