5 problems

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Browning's conjecture on a triple convolution sum of the divisor function
Browning's conjecture. Based on algebraic and geometric considerations, this sum is asymptotic to $c_hx(\log x)^3$ for a suitable constant $c_h\neq 0$ as $x\to\infty$ .
Conjectureopenanalytic-number-theory convolution-sums divisor-functionarXiv posted 2 days ago
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The kernel-growth conjecture for optimal OGF coefficients
Kernel-growth conjecture. An optimal ordinary generating function $\mathcal{C}(q)$ with integer-valued coefficients, $\mathcal{C}(0)\neq 0$ , that attains the theoretical maximum of…
Conjectureopenasymptotic-analysis convolution-sums generating-functionsarXiv posted 2 days ago
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The cross-correlation equivalence conjecture for convolution kernels
Equivalence conjecture. The statistic $\operatorname{Corr}_1(\mathcal{C},\mathcal{D})$ is maximized or minimized over all possible $\mathcal{C}(q)$ if and only if…
Conjectureopenconvolution-sums correlation-statistics generating-functionsarXiv posted 2 days ago
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The Euler-transform expansion conjecture for the optimal OGF
Euler-transform optimality conjecture. An optimal selection of $\mathcal{C}(q)$ has the expansions
Conjectureopenconvolution-sums euler-transform generating-functionsarXiv posted 2 days ago
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The optimal OGF conjecture for cross-correlation with a kernel
Optimal-OGF conjecture. An optimal ordinary generating function maximizing those correlation coefficients is
Conjectureopenconvolution-sums generating-functionsarXiv posted 2 days ago

5 problems

Browning's conjecture on a triple convolution sum of the divisor function

The kernel-growth conjecture for optimal OGF coefficients

The cross-correlation equivalence conjecture for convolution kernels

The Euler-transform expansion conjecture for the optimal OGF

The optimal OGF conjecture for cross-correlation with a kernel