L-functions as distributions

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Abstract

We define an axiomatic class of L-functions extending the Selberg class. We show in particular that one can recast the traditional conditions of an Euler product, analytic continuation and functional equation in terms of distributional identities akin to Weil’s explicit formula. The generality of our approach enables some new applications; for instance, we show that the L-function of any cuspidal automorphic representation of GL3(AQ) has infinitely many zeros of odd order.
Original languageEnglish
Pages (from-to)423-454
Number of pages32
JournalMathematische Annalen
Volume363
Issue number1
DOIs
Publication statusPublished - 8 Feb 2015

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