Notes

Some unpublished articles:

1. A Weighted Large Sieve Inequality
   • 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.
2. An estimate for the number of solutions of forms in prime variables
   • 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.

Here are some notes from talks and seminar presentations at the University of Münster and the University of Houston.

1. Elliptic Curves
2. Tate Module and the Weil Pairing
3. Law of Large Numbers and the Central Limit Theorem in Number Theory
4. Homogenization of Convex Integral Functionals Under Weakened Growth Conditions
5. Deep Neural Networks and the Analysis of the Approximation Error
6. Haar Measure and the Fourier Transform on Locally Compact Abelian Groups
7. A Computational Comparison of Lang–Trotter and Hardy–Littlewood Constants for CM Elliptic Curves