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Miniature of Sign changes of Fourier coefficients of Hilbert modular forms
Sign changes of Fourier coefficients of Hilbert modular forms

Date: 2014-01-01

Creator: Jaban Meher, Naomi Tanabe

Access: Open access

Sign changes of Fourier coefficients of various modular forms have been studied. In this paper, we analyze some sign change properties of Fourier coefficients of Hilbert modular forms, under the assumption that all the coefficients are real. The quantitative results on the number of sign changes in short intervals are also discussed. © 2014 Elsevier Inc.
Miniature of Determining hilbert modular forms by central values of rankin-selberg convolutions: The level aspect
Determining hilbert modular forms by central values of rankin-selberg convolutions: The level aspect

Date: 2017-12-01

Creator: Alia Hamieh, Naomi Tanabe

Access: Open access

In this paper, we prove that a primitive Hilbert cusp form g is uniquely determined by the central values of the Rankin-Selberg L-functions (formula presented), where f runs through all primitive Hilbert cusp forms of level q for infinitely many prime ideals q. This result is a generalization of the work of Luo (1999) to the setting of totally real number fields.
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