Premium
Picard–Fuchs equations for Shimura curves over Q
Author(s) -
Baba Srinath,
Granath Håkan
Publication year - 2021
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12430
Subject(s) - mathematics , transcendental number , modularity (biology) , property (philosophy) , modular form , abelian group , pure mathematics , computation , algebraic number , algebra over a field , modular design , complex multiplication , mathematical analysis , elliptic curve , algorithm , philosophy , genetics , epistemology , computer science , biology , operating system
We show that Picard–Fuchs equations of periods of certain families of abelian surfaces with quaternionic multiplication have fractional powers of algebraic modular forms as solutions. We give several applications of this modularity property, including a computation of exceptional sets of certain transcendental functions.