Anne-Maria Ernvall-Hytönen: On cusp forms, Fourier coefficients and exponential sums

I will briefly talk about modular forms in general, and cusp forms in particular. I will concentrate on exponential sums of their Fourier coefficients, and tell what we can say about them (both in theory and in practice: I will show some theorems and some pictures about computations), and I also try to explain why certain problems are extremely difficult.