Year: 2003
Type: preprint
Abstract: Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in $\SL(2,\ZZ)$. It is proved that such functions have a rotation-invariant limit distribution when the argument approaches the real axis. An example for a holomorphic almost modular form is the logarithm of $\prod_{n=1}^\infty (1-\exp(2\piın^2 z))$. The paper is motivated by the author's studies [J. Marklof, Int. Math. Res. Not. {\bf 39} (2003) 2131-2151] on the connection between almost modular functions and the distribution of the sequence $n^2x$ modulo one.
Source: arXiv (Cornell University)
Author: Marklof, Jens
Institution: University of Bristol
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949587472