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On the zeros of period functions associated to the Eisenstein series for Gamma(+)(0) (N)
- Authors
- Choi, SoYoung; Im, Bo-Hae
- Issue Date
- May-2022
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Period functions; Eisenstein series; N-self-inversive polynomials
- Citation
- JOURNAL OF NUMBER THEORY, v.234, pp.200 - 239
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF NUMBER THEORY
- Volume
- 234
- Start Page
- 200
- End Page
- 239
- ISSN
- 0022-314X
- Abstract
- We consider the period functions associated to the Eisenstein series for the Fricke group Gamma(+)(0) (N), the odd parts of the period functions and certain polynomials obtained from the period functions for Gamma(+)(0) (N), and we prove that all zeros of each of them lie on the circle |z| = 1/root N by applying the properties of a self-inversive polynomial. In particular, our result proves Berndt and Straub's suggested problem. (c) 2021 Elsevier Inc. All rights reserved.
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