A note on small gaps between nonzero Fourier coefficients of cusp forms (Q2796699)

In this work, the authors consider the problem of small gaps between nonzero Fourier coefficients of cusp forms. They prove that there are infinitely many primitive cusp forms \(f\) of weight \(2\) with the property that for all \(X\) large enough, every interval \((X,X+cX^{\frac{1}{4}})\) for \(c>0\) depending only on the form, contains an integer \(n\) such that the \(n^{\text{th}}\) Fourier coefficient of \(f\) is nonzero.