On the transcendence of certain Petersson inner products

Document Type: Special Issue of BIMS in Honor of Professor Freydoon Shahidi

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Abstract

‎We show that for all normalized Hecke eigenforms $f$‎ ‎with weight one and of CM type‎, ‎the number $(f,f)$ where $(\cdot‎, ‎\cdot )$ denotes‎ ‎the Petersson inner product‎, ‎is a linear form in logarithms and‎ ‎hence transcendental‎.

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