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On the sign changes of Dirichlet coefficients of triple product L-functions
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 4 / December 2024
- Published online by Cambridge University Press:
- 14 November 2024, pp. 1092-1106
- Print publication:
- December 2024
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- Article
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Let f and g be two distinct normalized primitive holomorphic cusp forms of even integral weight
$k_{1}$ and 
$k_{2}$ for the full modular group 
$SL(2,\mathbb {Z})$, respectively. Suppose that 
$\lambda _{f\times f\times f}(n)$ and 
$\lambda _{g\times g\times g}(n)$ are the n-th Dirichlet coefficient of the triple product L-functions 
$L(s,f\times f\times f)$ and 
$L(s,g\times g\times g)$. In this paper, we consider the sign changes of the sequence 
$\{\lambda _{f\times f\times f}(n)\}_{n\geq 1}$ and 
$\{\lambda _{f\times f\times f}(n)\lambda _{g\times g\times g}(n)\}_{n\geq 1}$ in short intervals and establish quantitative results for the number of sign changes for 
$n \leq x$, which improve the previous results.
