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 Ïµ> 0 and a primitive adelic Hilbert cusp form f of weight k= (k1, k2, â�¦ , kn) â�� (2 Z) n and full level, there exists an integral ideal m with N(m)â�ªÏµQf9/20+Ïµ 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)â�ªÏµQf1/2+Ïµ such that Cf(m) < 0. We also prove that when k= (k1, k2, â�¦ , kn) â�� (2 Z) n, asymptotically half of the Fourier coefficients are positive while half are negative.

Item Type: | Journal Article |
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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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