A nontrivial bound is proved for the average shifted convolution sum B(H,N) of Fourier coefficients of Hecke-Maass cusp forms on GL(d1) x GL(d2) for H at least N^{1-4/(d1+d2)+eps}.
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Proves asymptotic for second moment of GL(n)×GL(n+1) Rankin-Selberg L(1/2, Π⊗π) with Π varying by conductor, and infinitely many Π with simultaneous non-vanishing for two fixed π1, π2.
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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Average shifted convolution sum for $GL(d_1)\times GL(d_2)$
A nontrivial bound is proved for the average shifted convolution sum B(H,N) of Fourier coefficients of Hecke-Maass cusp forms on GL(d1) x GL(d2) for H at least N^{1-4/(d1+d2)+eps}.
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Moments of $L$-functions via a relative trace formula
Proves asymptotic for second moment of GL(n)×GL(n+1) Rankin-Selberg L(1/2, Π⊗π) with Π varying by conductor, and infinitely many Π with simultaneous non-vanishing for two fixed π1, π2.
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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.