Samuel Holmin: Explicit bounds for the class number of imaginary quadratic fields, Part II

We will complete the proof from last time.

Siegel's theorem states a lower bound for the class number h(-d) for negative fundamental discriminants -d, but it is given in terms of a constant which depends on a hypothetical counterexample to the generalized Riemann hypothesis, and can thus not give us any explicit numerical upper or lower bound for h(-d) for any given d. Following a recent paper by Soundarajan, I will in this talk derive explicit upper and lower bounds for the class number h(-d), conditional on GRH.