Holomorphic almost modular forms

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Holomorphic almost modular forms are holomorphic functions of the complex upper half plane that 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. AD example of a holomorphic almost modular form is the logarithm of Pi(n=1)(infinity) (1 - exp (2pi i n(2)z)). The paper is motivated by the author's previous studies [Int. Math. Res. Not. 39 (2003) 2131-2151] on the connection between almost modular functions and the distribution of the sequence n(2)x modulo one.
Translated title of the contributionHolomorphic almost modular forms
Original languageEnglish
Article numberPart 5
Pages (from-to)647 - 655
Number of pages9
JournalBulletin of the London Mathematical Society
Publication statusPublished - Sep 2004

Bibliographical note

Publisher: London Mathematical Society
Other identifier: IDS Number: 857KM

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