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Triple Correlation Sums of Coefficients of Cusp Forms

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 نشر من قبل David Lowry-Duda
 تاريخ النشر 2019
  مجال البحث
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We produce nontrivial asymptotic estimates for shifted sums of the form $sum a(h)b(m)c(2m-h)$, in which $a(n),b(n),c(n)$ are un-normalized Fourier coefficients of holomorphic cusp forms. These results are unconditional, but we demonstrate how to strengthen them under the Riemann Hypothesis. As an application, we show that there are infinitely many three term arithmetic progressions $n-h, n, n+h$ such that $a(n-h)a(n)a(n+h) eq 0$.



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