Title: Introduction to Hilbert modular forms and its determination by square-free Fourier coefficients.
Speaker: Rishabh Agnihotri
Let $\mathbf{f}$ be as above with $C_{\mathbf{f}}(\mathfrak{m})$ denote its Fourier coefficients. Then there exists a square-free ideal $\mathfrak{m}$ with $N(\mathfrak{m})\ll k_0^{3n+\epsilon}N(\mathfrak{n})^{\frac{6n^2+1}{2}+\epsilon}$ such that $C_{\mathbf{f}}(\mathfrak{m})\neq 0$. The implied constant depends only on $\epsilon, F$.