Conditionally on a twisted Linnik-Selberg-type conjecture for sums of Salié sums, the local square mean of the error in the hyperbolic circle problem for the modular group improves beyond exponent 9/14.
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Local square mean in the hyperbolic circle problem and sums of Sali\'e sums
Conditionally on a twisted Linnik-Selberg-type conjecture for sums of Salié sums, the local square mean of the error in the hyperbolic circle problem for the modular group improves beyond exponent 9/14.