In a paper published in 1959, Shimura presented an elegant calculation of the critical values of -functions attached to elliptic modular forms using the first cohomology group. We will show that a similar calculation is possible for Hilbert modular forms over real quadratic fields using the second cohomology group. We present explicit numerical examples calculated by this method.
"Cohomology and -values." Kyoto J. Math. 52 (2) 369 - 432, Summer 2012. https://doi.org/10.1215/21562261-1551003