Twisted A-harmonic sums are partial sums of a class of zeta values introduced by the first author. We prove some new identities for such sums and we deduce properties of analogues of finite zeta values in the framework of the Carlitz module. In the theory of finite multiple zeta values as introduced by Kaneko and Zagier, finite zeta values are all zero and there is no known non-zero finite multiple zeta value. In the Carlitzian setting the phenomenology is different as we can deduce, from our results, the irrationality of certain finite zeta values.

On twisted A-harmonic sums and Carlitz finite zeta values / Pellarin, F.; Perkins, R.. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 232:(2021), pp. 355-378. [10.1016/j.jnt.2018.10.018]

On twisted A-harmonic sums and Carlitz finite zeta values

Pellarin F.;
2021

Abstract

Twisted A-harmonic sums are partial sums of a class of zeta values introduced by the first author. We prove some new identities for such sums and we deduce properties of analogues of finite zeta values in the framework of the Carlitz module. In the theory of finite multiple zeta values as introduced by Kaneko and Zagier, finite zeta values are all zero and there is no known non-zero finite multiple zeta value. In the Carlitzian setting the phenomenology is different as we can deduce, from our results, the irrationality of certain finite zeta values.
2021
A-harmonic sums; Carlitz module; multiple zeta values
01 Pubblicazione su rivista::01a Articolo in rivista
On twisted A-harmonic sums and Carlitz finite zeta values / Pellarin, F.; Perkins, R.. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 232:(2021), pp. 355-378. [10.1016/j.jnt.2018.10.018]
File allegati a questo prodotto
File Dimensione Formato  
Pellarin_preprint_On-twisted_2021.pdf

accesso aperto

Note: Articolo in versione finale non disponibile
Tipologia: Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 323.21 kB
Formato Adobe PDF
323.21 kB Adobe PDF
Pellarin_versione-editoriale_On-twisted_2021.pdf

accesso aperto

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 456.21 kB
Formato Adobe PDF
456.21 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1594659
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact