3 problems

The Weil–Petersson random prime geodesic conjecture
Weil–Petersson random prime geodesic conjecture. Theorem 1.1 still holds after replacing the exponent $3/4$ by $1/2$ ; equivalently, there is a universal constant $c>0$ such that fo…
openFrom papersmoduli-spaces prime-geodesic-theorem weil-petersson-geometry
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6
The conjectural bound for the spectral exponential sum over the Picard manifold
Let $\Gamma=\mathrm{PSL}_{2}(\mathcal{O})$ , let $\lambda_j=1+t_j^2$ be the eigenvalues of the hyperbolic Laplacian on $\Gamma\backslash\mathfrak{h}^{3}$ , and let $S(T,X)$ be the sp…
openFrom papersautomorphic-forms prime-geodesic-theorem spectral-theory
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6
Integrality and nonnegativity of the hypergeometric coefficients $X^{(d)}_{m,h}(n;\mu)$
The quantities $X^{(d)}_{m,h}(n;\mu)$ are defined by the explicit formula preceding these observations, for the parameters and partition $\mu$ used there. Integrality conjecture. I…
openFrom papersdiscrete-tori number-theory prime-geodesic-theorem
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4

The Weil–Petersson random prime geodesic conjecture