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.
Hilbert’s Inequality.J
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For random hyperbolic surfaces of large genus, the variance of the weighted count of closed geodesics in short intervals [X, X+H] with H=o(X) is asymptotically 2H log X as genus tends to infinity.
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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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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Closed geodesics in short intervals for random hyperbolic surfaces
For random hyperbolic surfaces of large genus, the variance of the weighted count of closed geodesics in short intervals [X, X+H] with H=o(X) is asymptotically 2H log X as genus tends to infinity.
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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.