2 problems

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The nonvanishing and square-root bound conjecture for modular-symbol Ramanujan sums
Let $R_j^+(n)$ denote the scalar quantity associated with the embedded spectral contribution, and let $r(X)$ be the corresponding error term in the twisted Ramanujan-sum asymptotic…
Conjectureopenmodular-symbols ramanujan-sums spectral-theoryarXiv posted 2 days ago
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The arithmetic correlations conjecture for convolutions of divisor sums
Arithmetic correlations conjecture. There are numbers $\phi<1$ and $\psi>0$ such that
Conjectureopenarithmetic-correlations divisor-sums ramanujan-sumsarXiv posted 2 days ago

The nonvanishing and square-root bound conjecture for modular-symbol Ramanujan sums