see the details error message you got
Type of conditional expression cannot be determined because there is no implicit conversion between '<null>' and 'int'
you can fix this issue by changing your code as follows
int buzzInfluence = 0;
int.TryParse(Request.QueryString["buzzInfluence"], out buzzInfluence);
int? z = string.IsNullOrWhiteSpace(Request.QueryString["buzzInfluence"]) ? null : (int?)buzzInfluence;
int? zz = string.IsNullOrWhiteSpace(Request.QueryString["buzzInfluence"]) ? (int?)null : buzzInfluence;
you have to modify your code by adding
(int?)buzzInfluence
or
(int?)null
also, here are some more alternatives
int? zzz = string.IsNullOrWhiteSpace(Request.QueryString["buzzInfluence"]) ? default(int?) : buzzInfluence;
int? zzzz = string.IsNullOrWhiteSpace(Request.QueryString["buzzInfluence"]) ? new int?() : buzzInfluence;