LIMITS OF TRACES OF SINGULAR MODULI
- Authors
- Choi, Dohoon; Lim, Subong
- Issue Date
- 1월-2020
- Publisher
- AMER MATHEMATICAL SOC
- Keywords
- Modular traces; regularized L-functions; Eichler-Shimura cohomology theory
- Citation
- TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.373, no.1, pp.185 - 227
- Indexed
- SCIE
SCOPUS
- Journal Title
- TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
- Volume
- 373
- Number
- 1
- Start Page
- 185
- End Page
- 227
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/58495
- DOI
- 10.1090/tran/7890
- ISSN
- 0002-9947
- Abstract
- Let f and g be weakly holomorphic modular functions on Gamma(0)(N) with the trivial character. For an integer d, let Tr-d(f) denote the modular trace of f of index d. Let r be a rational number equivalent to i infinity under the action of Gamma(0)(4N). In this paper, we prove that when z goes radially to r, the limit Q((H) over cap (f))(r) of the sum H(f)(z) = Sigma(d>0) Tr-d(f)e(2 pi idz) is a special value of a regularized twisted L-function defined by Tr-d(f) for d <= 0. It is proved that the regularized L-function is meromorphic on C and satisfies a certain functional equation. Finally, under the assumption that N is square free, we prove that if Q((H) over cap (f))(r) = Q((H) over cap (g))(r) for all r equivalent to i infinity under the action of Gamma(0)(4N), then Tr-d(f) = Tr-d(g) for all integers d.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Science > Department of Mathematics > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.