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Bounds for standard $L$-functions

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arxiv 2109.15230 v3 pith:GYUD6G4V submitted 2021-09-30 math.NT

Paul D. Nelson This is my paper · ORCID
classification math.NT
keywords aspectstandardaddressautomorphicboundboundscasecuspidal
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abstract

Let $\pi$ be a cuspidal automorphic representation of a general linear group over the rational numbers. We establish a subconvex bound for the standard $L$-function of $\pi$ in the $t$-aspect. More generally, we address the spectral aspect in the case of uniform parameter growth.

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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. On the spectral aspect density hypothesis and application

    math.NT 2025-04 accept novelty 8.0 of 10

    For n >= 4, the paper establishes Sarnak's density hypothesis in the spectral aspect for GL_n(Z) cuspidal representations and uses it to prove the Diophantine exponent of the SL_n(Z[1/p])-action is optimal (kappa = 1).

  2. Level aspect subconvexity for $\textrm{GL(2)}\times \textrm{GL(2)}$ $\textrm{L}$-functions

    math.NT 2024-12 conditional novelty 7.0 of 10

    L(1/2, f⊗g) ≤ p^{1/2 - 1/524 + ε} for newforms f of prime level p with any nebentypus and fixed eigenforms g, improving the prior δ = 1/1413.

  3. 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}}.

  4. 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.

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