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arXiv · 1707.01576

Subconvexity for modular form L-functions in the t aspect

Andrew R. Booker·Micah B. Milinovich·Nathan Ng
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Abstract

Modifying a method of Jutila, we prove a t aspect subconvexity estimate for L-functions associated to primitive holomorphic cusp forms of arbitrary level that is of comparable strength to Good's bound for the full modular group, thus resolving a problem that has been open for 35 years. A key innovation in our proof is a general form of Voronoi summation that applies to all fractions, even when the level is not squarefree.

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Andrew R. Booker, Micah B. Milinovich, Nathan Ng. 2017-07-05. Subconvexity for modular form L-functions in the t aspect. https://doi.org/10.1016/j.aim.2018.10.037

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