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Maass form twisted Shintani $ \mathcal{L}$-functions


Author: Bob Hough
Journal: Proc. Amer. Math. Soc. 145 (2017), 4161-4174
MSC (2010): Primary 11E45; Secondary 11M41, 11F72
DOI: https://doi.org/10.1090/proc/13563
Published electronically: April 6, 2017
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Abstract: The Maass form twisted Shintani $ \mathcal {L}$-functions are introduced, and some of their analytic properties are studied. These functions contain data regarding the distribution of shapes of cubic rings.


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Additional Information

Bob Hough
Affiliation: School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540
Address at time of publication: Department of Mathematics, Stony Brook University, 100 Nicolls Drive, Stony Brook, New York 11794
Email: robert.hough@stonybrook.edu

DOI: https://doi.org/10.1090/proc/13563
Keywords: Equidistribution, Shintani zeta function, Maass form
Received by editor(s): June 2, 2016
Received by editor(s) in revised form: October 31, 2016
Published electronically: April 6, 2017
Additional Notes: This material was based upon work supported by the National Science Foundation under agreement No. DMS-1128155. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
This work was partially supported by ERC Grant 279438, Approximate Algebraic Structure and Applications.
This work was partially supported by the AIM Square on alternative proofs of the Davenport-Heilbronn Theorems.
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

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