Author:
Nandi Rimpa,Singh Sujeet Kumar,Tiwari Prashant
Abstract
AbstractWe prove a quantitative result for the number of sign changes of the Fourier coefficients of a Hermitian cusp form of degree 2. In addition, we prove a quantitative result for the number of sign changes of the primitive Fourier coefficients. We give an explicit upper bound for the first sign change of the Fourier coefficients of a Hermitian cusp form of degree 2 over certain imaginary quadratic extensions.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference22 articles.
1. Anamby, P., Das, S.: Distinguishing Hermitian cusp forms of degree $$2$$ by a certain subset of all Fourier coefficients. Publ. Mat. 63, 307–341 (2019)
2. Choie, Y., Kohnen, W.: The first sign change of Fourier coefficients of cusp forms. Am. J. Math. 131, 517–543 (2009)
3. Choie, Y., Gun, S., Kohnen, W.: An explicit bound for the first sign change of the Fourier coefficients of a Siegel cusp form. Int. Math. Res. Not. 2014, 3782–3792 (2015)
4. Dern, T., Krieg, A.: Graded rings of Hermitian modular forms of degree 2. Manuscr. Math. 110, 251–272 (2003)
5. Dern, T., Krieg, A.: The graded ring of Hermitian modular forms of degree 2 over $${\mathbb{Q} }(\sqrt{-2})$$. J. Number Theory 107, 241–265 (2004)