The Taylor coefficients of weight k Eisenstein series wrt. SL₂(Z) are related to values of L-functions for Hecke characters in the point k. We show some congruences for Taylor coefficients of Eisenstein series of weight 4 and 6 and use them to establish congruences for values of L-functions for Hecke characters in the points 4 and 6. It is well known, that all zeros of the Eisenstein series E_k wrt. SL₂(Z) in the standard fundamental domain has modulus 1. We show that this is also true for #ⁿ E_k, where # is a certain differential operator. We then proceed to study logarithms of multiplier systems. For automorphic forms wrt. Hecke triangle groups and Fuchsian groups with no elliptic elements and genus 0, we show that some logarithms of multiplier systems can be interpreted as a linking number. Finally we show a "twisted" version of the prime geodesics theorem, and logarithms of multiplier systems.