On the zeros of period functions associated to the Eisenstein series for Γ0+(N)

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We consider the period functions associated to the Eisenstein series for the Fricke group gamma(+& nbsp;)(0) (N), the odd parts of the period functions and certain polynomials obtained from the period functions for gamma(+& nbsp;)(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)& nbsp;2021 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2022-05
Language
English
Article Type
Article
Citation

JOURNAL OF NUMBER THEORY, v.234, pp.200 - 239

ISSN
0022-314X
DOI
10.1016/j.jnt.2021.06.021
URI
http://hdl.handle.net/10203/296713
Appears in Collection
MA-Journal Papers(저널논문)
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