TY - JOUR
T1 - A theta expression of the Hilbert modular functions for √ 5 via the periods of K3 surfaces
AU - Nagano, Atsuhira
PY - 2013/12
Y1 - 2013/12
N2 - In this paper, we give an extension of the classical story of the elliptic modular function to the Hilbertmodular case forQ( √ 5).We construct the period mapping for a family F = {S(X,Y )} ofK3 surfaces with 2 complex parametersX and Y . The inverse correspondence of the period mapping gives a system of generators of Hilbert modular functions forQ( √ 5). Moreover, we show an explicit expression of this inverse correspondence by theta constants.
AB - In this paper, we give an extension of the classical story of the elliptic modular function to the Hilbertmodular case forQ( √ 5).We construct the period mapping for a family F = {S(X,Y )} ofK3 surfaces with 2 complex parametersX and Y . The inverse correspondence of the period mapping gives a system of generators of Hilbert modular functions forQ( √ 5). Moreover, we show an explicit expression of this inverse correspondence by theta constants.
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U2 - 10.1215/21562261-2366102
DO - 10.1215/21562261-2366102
M3 - Article
AN - SCOPUS:84888394553
SN - 2156-2261
VL - 53
SP - 815
EP - 843
JO - Kyoto Journal of Mathematics
JF - Kyoto Journal of Mathematics
IS - 4
ER -