On the signs of Fourier coefficients of Hilbert cusp forms

Pal, R (2020) On the signs of Fourier coefficients of Hilbert cusp forms. In: Ramanujan Journal .

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Abstract

We prove that given any ϵ> 0 and a primitive adelic Hilbert cusp form f of weight k= (k1, k2, � , kn) � (2 Z) n and full level, there exists an integral ideal m with N(m)�ϵQf9/20+ϵ such that the m-th Fourier coefficient of Cf(m) of f is negative. Here n is the degree of the associated number field, N(m) is the norm of integral ideal m and Qf is the analytic conductor of f. In the case of arbitrary weights, we show that there is an integral ideal m with N(m)�ϵQf1/2+ϵ such that Cf(m) < 0. We also prove that when k= (k1, k2, � , kn) � (2 Z) n, asymptotically half of the Fourier coefficients are positive while half are negative.

Item Type:	Journal Article
Publication:	Ramanujan Journal
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	17 Feb 2020 11:38
Last Modified:	17 Feb 2020 11:38
URI:	http://eprints.iisc.ac.in/id/eprint/64531

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