Zobrazeno 1 - 10
of 200
pro vyhledávání: '"Marklof, Jens"'
Autor:
Marklof, Jens, Pollicott, Mark
We prove extreme value laws for cusp excursions of the horocycle flow in the case of surfaces of constant negative curvature. The key idea of our approach is to study the hitting time distribution for shrinking Poincar\'e sections that have a particu
Externí odkaz:
http://arxiv.org/abs/2408.01781
Autor:
Marklof, Jens, Monk, Laura
Rudnick recently proved that the spectral number variance for the Laplacian of a large compact hyperbolic surface converges, in a certain scaling limit and when averaged with respect to the Weil-Petersson measure on moduli space, to the number varian
Externí odkaz:
http://arxiv.org/abs/2407.10778
Autor:
Marklof, Jens
We construct a point set in the Euclidean plane that elucidates the relationship between the fine-scale statistics of the fractional parts of $\sqrt n$ and directional statistics for a shifted lattice. We show that the randomly rotated, and then stre
Externí odkaz:
http://arxiv.org/abs/2406.09107
Autor:
Marklof, Jens
This paper studies the logarithmic moments of the smallest denominator of all rationals in a shrinking interval with random center. Convergence follows from the more general results in [arXiv:2310.11251, Bull. Lond. Math. Soc., to appear], and the ke
Externí odkaz:
http://arxiv.org/abs/2312.15303
Autor:
Marklof, Jens
We establish higher dimensional versions of a recent theorem by Chen and Haynes [Int. J. Number Theory 19 (2023), 1405-1413] on the expected value of the smallest denominator of rational points in a randomly shifted interval of small length, and of t
Externí odkaz:
http://arxiv.org/abs/2310.11251
Autor:
Marklof, Jens, Welsh, Matthew
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 linear term in the exponent, the estimates can be further improved for
Externí odkaz:
http://arxiv.org/abs/2305.06995
Autor:
Kim, Wooyeon, Marklof, Jens
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. Furthermore, we show that the pair correlation function is Poissonian for any ir
Externí odkaz:
http://arxiv.org/abs/2302.13308
Autor:
Marklof, Jens, Welsh, Matthew
Theta sums are finite exponential sums with a quadratic form in the oscillatory phase. This paper establishes new upper bounds for theta sums in the case of smooth and box truncations. This generalises a classic 1977 result of Fiedler, Jurkat and K\"
Externí odkaz:
http://arxiv.org/abs/2108.01040
Autor:
Marklof, Jens, Welsh, Matthew
Publikováno v:
Duke Math. J. 172 (12) 2303 - 2364, 1 September 2023
We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence $\mu^2 \equiv D \bmod m$, with $D > 0$ square-free and $D\not\equiv 1 \bmod 4$. This is achieved by translating the problem to convergence of cer
Externí odkaz:
http://arxiv.org/abs/2105.02854