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arXiv · 2004.00284

A unified scheme of approach to the Ramanujan conjecture

Andre Unterberger
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Abstract

The Ramanujan conjecture for modular forms of holomorphic type was proved by Deligne almost half a century ago: the proof, based on his earlier proof of Weil's conjectures, was an achievement of algebraic geometry. We give here a short analytic proof of the Ramanujan-Deligne theorem, and we shall indicate at the end the close analogy of the proof with that of the Ramanujan-Petersson conjecture for Maass forms [8].

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Andre Unterberger. 2020-04-01. A unified scheme of approach to the Ramanujan conjecture. https://arxiv.org/abs/2004.00284

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