Eisenstein series whose Fourier coefficients are zeta functions of binary Hermitian forms
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- by Jorge Flórez, Cihan Karabulut and An Hoa Vu
- Proc. Amer. Math. Soc. 148 (2020), 4179-4187
- DOI: https://doi.org/10.1090/proc/15070
- Published electronically: May 22, 2020
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Abstract:
In this paper we investigate a result of Ueno on the modularity of generating series associated to the zeta functions of binary Hermitian forms previously studied by Elstrodt et al. We improve his result by showing that the generating series are Eisenstein series. As a consequence we obtain an explicit formula for the special values of zeta functions associated with binary Hermitian forms.References
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Bibliographic Information
- Jorge Flórez
- Affiliation: Department of Mathematics, Borough of Manhattan Community College, City University of New York, 199 Chambers Street, New York, New York 10007
- Email: jflorez@bmcc.cuny.edu
- Cihan Karabulut
- Affiliation: Department of Mathematics, William Paterson University, Wayne, New Jersey 07470
- MR Author ID: 1335068
- Email: karabulutc@wpunj.edu
- An Hoa Vu
- Affiliation: Department of Mathematics, The Graduate Center, City University of New York, New York, New York 10016
- MR Author ID: 1308085
- Email: avu@gradcenter.cuny.edu
- Received by editor(s): August 16, 2019
- Received by editor(s) in revised form: February 14, 2020
- Published electronically: May 22, 2020
- Additional Notes: The second author was partly supported by the Assigned Release Time (ART) program for research from William Paterson University
- Communicated by: Amanda Folsom
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 4179-4187
- MSC (2010): Primary 11F30, 11M36; Secondary 32N10
- DOI: https://doi.org/10.1090/proc/15070
- MathSciNet review: 4135287