Non-vanishing and sign changes of Hecke eigenvalues for half-integral weight cusp forms

作者：Chen, B.; Wu, J.^*

来源：Indagationes Mathematicae, 2016, 27(2): 488-505.

DOI：10.1016/j.indag.2016.01.001

• Forms of half-integer weight
• Fourier coefficients of automorphic forms
• Exponential sums
• B-free numbers

In this paper, we consider three problems about signs of the Fourier coefficients of a cusp form f with half-integral weight: @@@ - The first negative coefficient of the sequence fat {a(f)(tn(2))}(n is an element of N), @@@ - The number of coefficients a(f)(tn(2)) of same signs, @@@ - Non-vanishing of coefficients a(f)(tn(2)) in short intervals and in arithmetic progressions, @@@ where a(f)(n) is the nth Fourier coefficient of f and t is a square-free integer such that a(f)(t) not equal 0.

• 出版日期2016-3
• 单位山东大学; 渭南师范学院; 同济大学