L-functions as distributions

Andrew Booker

doi:10.1007/s00208-015-1178-z

L-functions as distributions

Andrew Booker

Research output: Contribution to journal › Article (Academic Journal) › peer-review

6 Citations (Scopus)

288 Downloads (Pure)

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(A_Q) has infinitely many zeros of odd order.

Original language	English
Pages (from-to)	423-454
Number of pages	32
Journal	Mathematische Annalen
Volume	363
Issue number	1
DOIs	https://doi.org/10.1007/s00208-015-1178-z
Publication status	Published - 8 Feb 2015

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10.1007/s00208-015-1178-z

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Springer Verlag at http://dx.doi.org/10.1007/s00208-015-1178-z. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 330 KB

http://arxiv.org/abs/1308.3067v2

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Detecting squarefree numbers
Booker, A. R. (Principal Investigator)
1/07/13 → 1/07/15
Project: Research
Explicit number theory, automorphic forms and L-functions
Booker, A. R. (Principal Investigator)
1/10/09 → 1/04/15
Project: Research

Professor Andrew R Booker
- Andrew.Bookerbristol.acuk
- School of Mathematics - Professor of Pure Mathematics
Person: Academic

Cite this

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title = "L-functions as distributions",

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{\textquoteright}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.",

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AB - 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.

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L-functions as distributions

Abstract

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Projects

Detecting squarefree numbers

Explicit number theory, automorphic forms and L-functions

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Professor Andrew R Booker

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