We present a formula describing modularity gap for Eisenstein series, which is written in terms of a certain double series. Limit values of the gap at nonzero rational points are expressible by Hurwitz zeta values. Our gap estimates near the origin are applied to examining the asymptotic behaviour of Ramanujan q-series and q-zeta values near the natural boundary |q|=1.
"Modularity gap for Eisenstein series." Proc. Japan Acad. Ser. A Math. Sci. 86 (4) 79 - 84, April 2010. https://doi.org/10.3792/pjaa.86.79