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The subconvexity problem for Rankin-Selberg and triple product L-functions

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arxiv 2207.14449 v2 pith:MDE3JYAS submitted 2022-07-29 math.NT

classification math.NT
keywords boundsconjecturesl-functionl-functionslocalproblemproductrankin-selberg
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In this paper we study the subconvexity problem for the Rankin-Selberg L-function and triple product L-function, allowing joint ramifications and conductor dropping range. We first extend the method of Michel-Venkatesh to reduce the bounds for L-functions to local conjectures on test vectors, then verify these local conjectures under certain conditions, giving new subconvex bounds as long as the representations are not completely related.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Squarefree numbers in short intervals: explicit and formalized

    math.NT 2026-08 conditional novelty 6.0 of 10

    For intervals of length H = X^{1/5 - 2/90935 + ε}, the number of squarefree integers differs from (6/π²)H by at most an explicit constant times H X^{-ε/10^{25}}.

  2. Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect

    math.NT 2025-09 conditional novelty 6.0 of 10

    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.

  3. Spectral Reciprocity and Hybrid Subconvexity Bound for triple product $L$-functions

    math.NT 2024-12 conditional novelty 5.0 of 10

    An explicit hybrid level-aspect subconvexity bound for triple product L-functions over number fields, with unconditional saving exponent 1/60, extends to joint ramification and conductor dropping.

  4. Spectral Reciprocity for the first moment of triple product $L$-functions and applications

    math.NT 2024-12 conditional novelty 5.0 of 10

    A twisted first moment of triple product L-functions satisfies a spectral reciprocity formula, yielding a level-aspect subconvexity bound with saving 225/2624 unconditionally.

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