ON POWER MOMENTS OF THE HECKE MULTIPLICATIVE FUNCTIONS

KALYAN CHAKRABORTY; MAKOTO MINAMIDE

doi:10.1017/S1446788715000063

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

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KALYAN CHAKRABORTY: Affiliation:
Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India email kalyan@hri.res.in
MAKOTO MINAMIDE*: Affiliation:
Faculty of Science, Kyoto Sangyo University, Kamigamo, Kyoto 603-8555, Japan email minamide@cc.kyoto-su.ac.jp Faculty of Science, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, Japan email minamide@yamaguchi-u.ac.jp
*: ✉minamide@cc.kyoto-su.ac.jp

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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.