Arithmetic Hilbert Modular Functions Ill

1986 ◽  
pp. 1-40
Author(s):  
Walter L. Baily
Keyword(s):  
Modular Functions ◽  
Hilbert Modular

CM-values of Hilbert modular functions

2005 ◽  
Vol 163 (2) ◽  
pp. 229-288 ◽  
Author(s):  
Jan Hendrik Bruinier ◽  
Tonghai Yang
Keyword(s):  
Modular Functions ◽  
Hilbert Modular

Real-dihedral harmonic Maass forms and CM-values of Hilbert modular functions

2016 ◽  
Vol 152 (6) ◽  
pp. 1159-1197
Author(s):  
Yingkun Li
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Hilbert Modular Forms ◽  
Algebraic Numbers ◽  
Modular Functions ◽  
Maass Forms ◽  
Stark's Conjecture ◽  
Hilbert Modular ◽  
Harmonic Maass Forms ◽  
The Individual

In this paper, we study real-dihedral harmonic Maass forms and their Fourier coefficients. The main result expresses the values of Hilbert modular forms at twisted CM 0-cycles in terms of these Fourier coefficients. This is a twisted version of the main theorem in Bruinier and Yang [CM-values of Hilbert modular functions, Invent. Math. 163 (2006), 229–288] and provides evidence that the individual Fourier coefficients are logarithms of algebraic numbers in the appropriate real-quadratic field. From this result and numerical calculations, we formulate an algebraicity conjecture, which is an analogue of Stark’s conjecture in the setting of harmonic Maass forms. Also, we give a conjectural description of the primes appearing in CM-values of Hilbert modular functions.

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