Subconvexity for GL(3)×GL(2) twists

Bounds for twists of GL(3) $L$-functions

“…Aggarwal [1], who revisited Munshi's work in [28] by removing the "conductor lowering" trick, was able to improve the exponent of saving in the t-aspect case to 3/40. The exponent of saving in the M-aspect was recently improved to 1/32 by Sharma [37]. Following Li's work in [17], there have been recent developments in the subconvexity problem on GL(3) × GL(2) in different aspects, and the reader is referred to [15,16,18,19,31,35,37,38].…”

“…The exponent of saving in the M-aspect was recently improved to 1/32 by Sharma [37]. Following Li's work in [17], there have been recent developments in the subconvexity problem on GL(3) × GL(2) in different aspects, and the reader is referred to [15,16,18,19,31,35,37,38].…”

Subconvexity bound for ${\rm GL}(2)$ $L$-functions: $t$-aspect

“…In this article, we yet again explore the subconvexity problem (ScP) for the degree six Rankin-Selberg GL(3) × GL(2) L-functions using Munshi's delta method [20]. This theme was initiated by Munshi [17] and was explored further by the second author and the third author along with Sharma, Mallesham, and various others (see [9], [10], [11], [12], [22]) to resolve subconvexity for these L-functions in various aspects (t, twist and spectral aspect). Apparently, the delta method approach so far has been more effective for L-functions associated with forms admitting a varying GL(1) factor, barring a few results (see [9], [10], [12]), where spectral parameters of a higher degree form vary, or levels of two higher degree forms vary simultaneously.…”