Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve

This paper draws connections between the double shuffle equations and structure of associators; universal mixed elliptic motives as defined by Hain and Matsumoto; and the Rankin-Selberg method for modular forms for $SL_2(\mathbb{Z})$. We write down explicit formulae for zeta elements $\sigma_{2n-1}$...

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Autor Principal: Brown, F
Formato: Journal article
Publicado: Cambridge University Press 2017
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author Brown, F
author_facet Brown, F
author_sort Brown, F
collection OXFORD
description This paper draws connections between the double shuffle equations and structure of associators; universal mixed elliptic motives as defined by Hain and Matsumoto; and the Rankin-Selberg method for modular forms for $SL_2(\mathbb{Z})$. We write down explicit formulae for zeta elements $\sigma_{2n-1}$ (generators of the Tannaka Lie algebra of the category of mixed Tate motives over $\mathbb{Z}$) in depths up to four, give applications to the Broadhurst-Kreimer conjecture, and completely solve the double shuffle equations for multiple zeta values in depths two and three
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spelling oxford-uuid:3dc9c8fb-8a5b-46b4-afe9-147e691733ed2022-03-26T14:21:32ZZeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curveJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3dc9c8fb-8a5b-46b4-afe9-147e691733edSymplectic Elements at OxfordCambridge University Press2017Brown, FThis paper draws connections between the double shuffle equations and structure of associators; universal mixed elliptic motives as defined by Hain and Matsumoto; and the Rankin-Selberg method for modular forms for $SL_2(\mathbb{Z})$. We write down explicit formulae for zeta elements $\sigma_{2n-1}$ (generators of the Tannaka Lie algebra of the category of mixed Tate motives over $\mathbb{Z}$) in depths up to four, give applications to the Broadhurst-Kreimer conjecture, and completely solve the double shuffle equations for multiple zeta values in depths two and three
spellingShingle Brown, F
Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve
title Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve
title_full Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve
title_fullStr Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve
title_full_unstemmed Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve
title_short Zeta elements in depth 3 and the fundamental Lie algebra of the infinitesimal Tate curve
title_sort zeta elements in depth 3 and the fundamental lie algebra of the infinitesimal tate curve
work_keys_str_mv AT brownf zetaelementsindepth3andthefundamentalliealgebraoftheinfinitesimaltatecurve