## Speaker:

Amita Malik

## Speaker Link:

## Institution:

Max Planck Institute

## Time:

Thursday, May 26, 2022 - 10:00am to 11:00am

## Location:

https://uci.zoom.us/j/95268809663

In this talk, we discuss the asymptotic behavior of the number of integer partitions into primes concerning a Chebotarev condition. In special cases, this reduces to the study of partitions into primes in arithmetic progressions. While the study for ordinary partitions goes back to Hardy and Ramanujan, partitions into primes have been re-visited recently. Our error term is sharp and in the particular case of partitions into prime numbers, we improve on a result of Vaughan. In connection with the monotonicity result of Bateman and Erd\H{o}s, we give an asymptotic formula for the difference of the number of partitions of positive integers which are k-apart.