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Proportion of modular forms with transcendental zeros for general levelsopen access
- Issue Date
- 1-Jan-2023
- Publisher
- JAPAN ACAD
- Keywords
- Modular form; transcendental zero; density
- Citation
- PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, v.99, no.2, pp.19 - 22
- Indexed
- SCIE
SCOPUS
- Volume
- 99
- Number
- 2
- Start Page
- 19
- End Page
- 22
- ISSN
- 0386-2194
- Abstract
- Let Gamma be a congruence subgroup such that Gamma(1)(N) subset of Gamma subset of Gamma(0)(N) for some positive integer N. For a positive integer k, let M-k,M-Z(Gamma) be the set of modular forms of weight k on Gamma with integral Fourier coefficients. Let R-k(Gamma) be the set of common zeros in the upper half plane H of all the modular forms of weight k on Gamma. In this note, we prove that the density of modular forms in M-k,M-Z(Gamma) with an algebraic zero z is not an element of R-k(Gamma) is zero.
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Related Researcher
- LIM, SU BONG
- Education (Mathematics Education)