A Burgess-type subconvexity bound for GL(2)xGL(2) L-functions holds uniformly in both spectral parameters when one form is dihedral or of level 1.
Balogh, Asymptotic expansions of the modified Bessel function of the third kind of imaginary order
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Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect
A Burgess-type subconvexity bound for GL(2)xGL(2) L-functions holds uniformly in both spectral parameters when one form is dihedral or of level 1.