| Summary: | In this paper, we study two-dimensional divisor problems of the Fourier coefficients of some automorphic product <i>L</i>-functions attached to the primitive holomorphic cusp form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> with weight <i>k</i> for the full modular group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><msub><mi>L</mi><mn>2</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">Z</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Additionally, we establish the upper bound and the asymptotic formula for these divisor problems on average, respectively.
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