Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Nordentoft, Asbjørn Christian"'
We prove that one hundred percent of closed geodesic periods of a Maa{\ss} form for the modular group are non-vanishing when ordered by length. We present applications to the non-vanishing of central values of Rankin--Selberg $L$-functions. Similar r
Externí odkaz:
http://arxiv.org/abs/2404.12982
We define new objects called 'horizontal $p$-adic $L$-functions' associated to $L$-values of twists of elliptic curves over $\mathbb{Q}$ by characters of $p$-power order and conductor prime to $p$. We study the fundamental properties of these objects
Externí odkaz:
http://arxiv.org/abs/2310.20678
We introduce a natural way of associating oriented closed geodesics on the modular curve to elements of $(\mathbb{Z}/q\mathbb{Z})^\times$ and prove that the corresponding packets associated to sufficiently large subgroups equidistribute in the unit t
Externí odkaz:
http://arxiv.org/abs/2305.18625
Duke, Imamo\={g}lu, and T\'oth have recently constructed a new geometric invariant, a hyperbolic orbifold, associated to each narrow ideal class of a real quadratic field. Furthermore, they have shown that the projection of these hyperbolic orbifolds
Externí odkaz:
http://arxiv.org/abs/2211.05890
In the present paper we study the central values of additive twists of Maa{\ss} forms $L$-series. In the case of the modular group, we show that the additive twists (when averaged over denominators) are asymptotically normally distributed. This suppl
Externí odkaz:
http://arxiv.org/abs/2208.14346
We prove that the homology classes of closed geodesics associated to subgroups of narrow class groups of real quadratic fields concentrate around the Eisenstein line. This fits into the framework of Duke's Theorem and can be seen as a real quadratic
Externí odkaz:
http://arxiv.org/abs/2203.06446
We study wide moments of Dirichlet $L$-functions using analytic properties of the Lerch zeta function. Among other things we obtain an asymptotic expansion of wide moments of Dirichlet $L$-functions (with arbitrary twists) extending results of Heath-
Externí odkaz:
http://arxiv.org/abs/2111.03834
Publikováno v:
Alg. Number Th. 18 (2024) 735-770
We calculate certain "wide moments" of central values of Rankin--Selberg $L$-functions $L(\pi\otimes \Omega, 1/2)$ where $\pi$ is a cuspidal automorphic representation of $\mathrm{GL}_2$ over $\mathbb{Q}$ and $\Omega$ is a Hecke character (of conduct
Externí odkaz:
http://arxiv.org/abs/2105.09130
Shifted convolution sums play a prominent r\^ole in analytic number theory. We investigate pointwise bounds, mean-square bounds, and average bounds for shifted convolution sums for Hecke eigenforms.
Comment: 22 pages. Final version to appear in
Comment: 22 pages. Final version to appear in
Externí odkaz:
http://arxiv.org/abs/2103.01248
We investigate the equidistribution of Hecke eigenforms on sets that are shrinking towards infinity. We show that at scales finer than the Planck scale they do not equidistribute while at scales more coarse than the Planck scale they equidistribute o
Externí odkaz:
http://arxiv.org/abs/2011.05810