Let f and g be two distinct Hecke–Maass cusp forms of weight zero for SL(2,Z)\documentclass[12pt]{minimal}
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\begin{document}$$SL(2,\mathbb {Z})$$\end{document} with Laplacian eigenvalues 14+u2\documentclass[12pt]{minimal}
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\begin{document}$$\frac{1}{4}+u^{2}$$\end{document} and 14+v2\documentclass[12pt]{minimal}
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\begin{document}$$\frac{1}{4}+v^{2}$$\end{document}, respectively. Let λf(n)\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _{f}(n)$$\end{document} and λg(n)\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _{g}(n)$$\end{document} be the real normalized Fourier coefficients satisfies λf(1)=λg(1)=1\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _{f}(1)=\lambda _{g}(1)=1$$\end{document}. Then in this paper we give a quantitative result concerning the sign changes of {λf(n)λg(n)}n∈N\documentclass[12pt]{minimal}
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\begin{document}$$\{\lambda _{f}(n)\lambda _{g}(n)\}_{n\in \mathbb {N}}$$\end{document} in a short interval. We refine the results given by Kumari and Sengupta (Ramanujan J 55:205–218, 2021) concerning the first sign change of the sequence {λf(n)λg(n)}n∈N\documentclass[12pt]{minimal}
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\begin{document}$$\{\lambda _{f}(n)\lambda _{g}(n)\}_{n\in \mathbb {N}}$$\end{document}.
