New logarithm laws and lattice point bounds yield a proof of power loss in the Mizohata-Takeuchi conjecture with explicit errors and establish genericity in C^k.
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3 Pith papers cite this work. Polarity classification is still indexing.
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Almost every point on affine subspaces in horospheres is Birkhoff generic except in cases of high Diophantine exponent or approximability by number-field subspaces.
An effective multi-equidistribution result for diagonal translates of unipotent flows is established, yielding a central limit theorem in inhomogeneous Diophantine approximation for non-Liouville shifts.
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Cusp Excursions, Lattice Points on Manifolds, and the Mizohata-Takeuchi Conjecture
New logarithm laws and lattice point bounds yield a proof of power loss in the Mizohata-Takeuchi conjecture with explicit errors and establish genericity in C^k.
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Birkhoff genericity on affine subspaces in horospheres
Almost every point on affine subspaces in horospheres is Birkhoff generic except in cases of high Diophantine exponent or approximability by number-field subspaces.