Vanishing properties of Fourier coefficients of holomorphic η-quotients

Key Points

• Fourier coefficients exhibit vanishing properties, suggesting deeper mathematical implications.
• The study focuses on both integral weight CM newforms and half-integral weight η-quotients.
• Examples include connections to Hurwitz class numbers and sums of squares in number theory.
• Insights from this investigation could advance understanding of modular forms and their applications.