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Sun, Hae-sang
Number Theory Group
Research Interests
  • Zeta function, L-function, mu invariant, indivisibility of special L-values

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GENERATION OF CYCLOTOMIC HECKE FIELDS BY MODULAR L-VALUES WITH CYCLOTOMIC TWISTS

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Title
GENERATION OF CYCLOTOMIC HECKE FIELDS BY MODULAR L-VALUES WITH CYCLOTOMIC TWISTS
Author
Sun, Hae-sang
Issue Date
2019-08
Publisher
JOHNS HOPKINS UNIV PRESS
Citation
AMERICAN JOURNAL OF MATHEMATICS, v.141, no.4, pp.907 - 940
Abstract
Let $p$ be an odd prime. We show that the compositum of the Hecke field of a normalized Hecke eigen cuspform for ${\rm GL}(2)$ over $\Bbb{Q}$ and a cyclotomic field of a $p$-power degree over $\Bbb{Q}$, namely the cyclotomic Hecke field, is generated by a single algebraic critical value of the corresponding $L$-function twisted by a Dirichlet character of sufficiently large $p$-power conductor when the level of cuspform is relatively prime to $p$. The same result holds when the level is divisible by $p$ if we assume further that the cuspform does not have an inner twist. This is a stronger version of a result of Luo-Ramakrishnan. As a consequence, we reformulate a result of H. Hida on the growth of Hecke fields in a Hida family, in terms of special $L$-values.
URI
https://scholarworks.unist.ac.kr/handle/201301/25607
URL
https://muse.jhu.edu/article/730009
DOI
10.1353/ajm.2019.0024
ISSN
0002-9327
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