- When Fourier analysis meets ergodic theory and number theory
- Project Year:
2024
- REU Student (s):
Abbas Dohadwala | Purdue University-Main Campus IN
| Ish Shah | Rutgers University-New Brunswick NJ
- Student 1 Institution:
Purdue University-Main Campus
- Student 2 Institution:
Rutgers University-New Brunswick
- Project Mentor:
Mariusz Mirek
- Project Mentor Area:
Mathematics
- Project Abstract:
Ergodic theory is an area of mathematics which studies the statistical properties of dynamical systems. The Birkhoff ergodic theorem is a classical result of ergodic theory, which establishes pointwise convergence almost everywhere for a specific average under certain conditions. In this project, we worked towards proving an ergodic theorem with some similarities, but involving fractional powers of primes. With techniques from analytic number theory and Fourier analysis, we studied exponential sums involving these fractional powers of primes to obtain certain bounds. Using these bounds, we use harmonic analysis tools to prove a sequence of theorems, eventually leading to our desired result.
