The paper describes a method to perform conditional analysis using GWAS summary data.
Corrigendum
Equation 4: by , we simply mean that in single-SNP based association analyses, the estimates of effect sizes do not take LD between SNPs into account. If two SNPs are in LD, there should be a sampling correlation between two beta estimates (sampling correlation = LD correlation under the null) but such correlation is ignored in single-SNP based analyses.
Equations 16 and 20: The terms highlighted in yellow should be dropped.