On binary additive problems with prime variables in short intervals

In this talk, we consider some asymptotic behaviour of binary additive
problems with prime variables in short intervals. We start with a
brief review on exceptional set estimates in short intervals and
continue to the recent work of Languasco and Zaccagnini on the short
interval asymptotic formulas. Although the preceding results were
mainly obtained via the circle method, we see that a more direct
method gives better results for some cases.