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ON POWER MOMENTS OF THE HECKE MULTIPLICATIVE FUNCTIONS

Part of: Elementary number theory Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  25 March 2015

KALYAN CHAKRABORTY  and
MAKOTO MINAMIDE
KALYAN CHAKRABORTY
Affiliation:
Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India email [email protected]
MAKOTO MINAMIDE*
Affiliation:
Faculty of Science, Kyoto Sangyo University, Kamigamo, Kyoto 603-8555, Japan email [email protected] Faculty of Science, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, Japan email [email protected]
*
✉[email protected]
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Abstract

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In a recent paper, Soundararajan has proved the quantum unique ergodicity conjecture by getting a suitable estimate for the second order moment of the so-called ‘Hecke multiplicative’ functions. In the process of proving this he has developed many beautiful ideas. In this paper we generalize his arguments to a general $k$th power and provide an analogous estimate for the $k$th power moment of the Hecke multiplicative functions. This may be of general interest.

Keywords

Hecke multiplicative functionsMaaß forms

MSC classification

Primary: 11F03: Modular and automorphic functions
Secondary: 11A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 3 , December 2015 , pp. 334 - 340
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Dusart, P., Autour de la fonction qui compte de nombre premiers (1998). Available athttp://www.unilim.fr/laco/theses/1998/T1998_01.pdf.Google Scholar
Soundararajan, K., ‘Quantum unique ergodicity for SL2(ℤ)∖ℍ’, Ann. of Math. (2) 172 (2010), 1529–1538.CrossRefGoogle Scholar