Holomorphic Almost Modular Forms
نویسنده
چکیده
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,Z). 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 ∏ ∞ n=1 (1− exp(2π inz)). The paper is motivated by the author’s studies [J. Marklof, Int. Math. Res. Not. 39 (2003) 2131-2151] on the connection between almost modular functions and the distribution of the sequence nx modulo one.
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