Establishes strong hybrid subconvexity bounds for twisted selfdual GL3 L-functions via a new GL3 x GL2 to GL4 x GL1 spectral reciprocity formula together with an averaged Lindelof bound on Dirichlet L-functions.
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Any number of primitive GL(1) and GL(2) L-functions can simultaneously take large values on the critical line unconditionally, improving prior conditional results.
Constructs equivariant isomorphisms Φ(P,P') between affinized cotangent bundles of Braverman-Kazhdan spaces for conjugate parabolics in SL_n, satisfying Coxeter relations via SL-gauge reflection functors on type A quiver varieties.
Partial results on low-lying zero densities imply explicit conditional lower bounds on central L-values, with bound quality tied to family symmetry type and allowed Fourier support.
Upper bounds on the least prime satisfying the Ramanujan conjecture simultaneously for two or three Hecke-Maass forms, and lower bounds on the natural density of primes satisfying it for at least one form in a given set.
citing papers explorer
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Strong Hybrid Subconvexity for Twisted Selfdual $\mathrm{GL}_3$ $L$-Functions
Establishes strong hybrid subconvexity bounds for twisted selfdual GL3 L-functions via a new GL3 x GL2 to GL4 x GL1 spectral reciprocity formula together with an averaged Lindelof bound on Dirichlet L-functions.
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Joint extreme values of $L$-functions on and off the critical line
Any number of primitive GL(1) and GL(2) L-functions can simultaneously take large values on the critical line unconditionally, improving prior conditional results.
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Quasi-Classical Braverman--Kazhdan Intertwiners via Quiver Varieties
Constructs equivariant isomorphisms Φ(P,P') between affinized cotangent bundles of Braverman-Kazhdan spaces for conjugate parabolics in SL_n, satisfying Coxeter relations via SL-gauge reflection functors on type A quiver varieties.
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A connection between low-lying zeros and central values of $L$-functions
Partial results on low-lying zero densities imply explicit conditional lower bounds on central L-values, with bound quality tied to family symmetry type and allowed Fourier support.
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On Ramanujan Primes for Hecke-Maass Cusp Forms
Upper bounds on the least prime satisfying the Ramanujan conjecture simultaneously for two or three Hecke-Maass forms, and lower bounds on the natural density of primes satisfying it for at least one form in a given set.