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math.NT2023
Bounds for theta sums in higher rank II
Jens Marklof, Matthew Welsh
In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a l…
math.NT2023
Poissonian pair correlation for directions in multi-dimensional affine lattices, and escape of mass estimates for embedded horospheres
Wooyeon Kim, Jens Marklof
We prove the convergence of moments of the number of directions of affine lattice vectors that fall into a small disc, under natural Diophantine conditions on the shift. Furthermor…