On linear relations between L-values and arithmetic functions

 In 1975 Cohen constructed a series of modular forms of half-integral weights. Its q-coefficients contain special values of Dirichlet functions and were used by Cohen to create various equations of them with arithmetic functions. The modular forms are called Cohen-Eisenstein series and were later generalized to the case for Hilbert modular forms. Making use of the generalized forms one can also write down linear equations for the special values of Dirichlet L-functions with respect to certain general real number fields, even in terms of arithmetic functions on rational integers. In this talk I would like to introduce how this works. The idea was originally inspired by Ikeda.