A Weighted Large Sieve Inequality
- I completed a research project under the supervision of Prof. Jan-Christoph Schlage-Puchta and proved a variant of the classical large sieve inequality by introducing suitable weight functions.
An estimate for the number of solutions of forms in prime variables (Draft)
- In 2021, J. Liu and L. Zhao proved the existence of solutions of a system of R forms with at least 4^{d+2}d^2R^5 prime variables. Using the Hardy-Littlewood Circle method they found an estimate for the number of such solutions which confirms the existence of prime solutions of a system of forms satisfying some local conditions. In this article, we obtain an unweighted estimate for R=1 using a minimalist approach derived by K. Biggs and J. Brandes. Supervisor: Prof. Julia Brandes