Paper Citation Record · LEDGER

Vanishing of Witten zeta function at negative integers

As of 23 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2412.11879.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.11879 v5

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T14:42:45.264134Z

measured 33 of 33 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

33 of 33 outbound references displayed

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verified fuzzy26
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External citation measurements

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Outbound references

Observation 357d2697-23d7-4d66-9aa1-fd5e3745dbd1 · outbound

This paper cites Convolution identities and lacunary recurrences for Bernoulli numbers.Journal of Number Theory, 124(1):105–122, 2007.

Vanishing of Witten zeta function at negative integers Convolution identities and lacunary recurrences for Bernoulli numbers.Journal of Number Theory, 124(1):105–122, 2007

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.882726Z

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Observation ac674c0b-cd5f-41c2-a279-eec144272eff · outbound

This paper cites Apostol.Introduction to analytic number theory.

Vanishing of Witten zeta function at negative integers Apostol.Introduction to analytic number theory

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.874830Z

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Observation b7bb3602-b09c-478e-bcd0-881fc1181a27 · outbound

This paper cites On single-variable Witten zeta functions of rank two and three.arXiv preprint arXiv:2412.17196, 2024.

Vanishing of Witten zeta function at negative integers On single-variable Witten zeta functions of rank two and three.arXiv preprint arXiv:2412.17196, 2024

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-08-11T14:42:45.649179Z

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Observation d32ba998-88fa-4d8b-b7ef-f5686b1127f4 · outbound

This paper cites Feasibility of the analytic continuationfλ + for certain polynomialsf.Functional Analysis and Its Applications, 2:85–87, 1968.

Vanishing of Witten zeta function at negative integers Feasibility of the analytic continuationfλ + for certain polynomialsf.Functional Analysis and Its Applications, 2:85–87, 1968

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.867462Z

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Observation 3f696fec-f6cf-49fa-a823-2bafec564a4e · outbound

This paper cites Chapters 4–6.

Vanishing of Witten zeta function at negative integers Chapters 4–6

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.859573Z

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Observation d926d3d6-11e1-4158-83bd-5b334a71794b · outbound

This paper cites an unresolved cited work.

Vanishing of Witten zeta function at negative integers Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-11T14:42:45.850867Z

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Observation 445dbc9b-0805-4217-93d6-2eeae7fc905c · outbound

This paper cites Polynomials associated to Lie algebras.arXiv preprint arXiv:2507.00326, 2025.

Vanishing of Witten zeta function at negative integers Polynomials associated to Lie algebras.arXiv preprint arXiv:2507.00326, 2025

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-08-11T14:42:45.488086Z

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Observation 4506a33b-b47e-476f-807b-c1491d20ea7b · outbound

This paper cites Number 33.

Vanishing of Witten zeta function at negative integers Number 33

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.842191Z

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Observation 2488702f-5e82-422a-b1a4-c08665c3fc20 · outbound

This paper cites Singularité de séries de Dirichlet associées à des polynômes de plusieurs variables et applications en théorie analytique des nombres.

Vanishing of Witten zeta function at negative integers Singularité de séries de Dirichlet associées à des polynômes de plusieurs variables et applications en théorie analytique des nombres

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.834553Z

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Observation 6ca99786-0ee3-4574-9e93-f5693d2d4a3f · outbound

This paper cites Values at non-positive integers of partially twisted multiple zeta-functions II.

Vanishing of Witten zeta function at negative integers Values at non-positive integers of partially twisted multiple zeta-functions II

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-11T14:42:45.302921Z

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Observation b848f422-845b-4aef-a3a0-525a7503248f · outbound

This paper cites Shintani–Barnes zeta and gamma functions.Advances in Mathemat- ics, 187(2):362–395, 2004.

Vanishing of Witten zeta function at negative integers Shintani–Barnes zeta and gamma functions.Advances in Mathemat- ics, 187(2):362–395, 2004

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.825242Z

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Observation 1a0dbe5b-7559-4b22-957c-9e31ae63a7e9 · outbound

This paper cites The representation zeta function of a FAb compactp-adic Lie group vanishes at−2.Bulletin of the London Mathematical Society, 46(2):239–244, 2014.

Vanishing of Witten zeta function at negative integers The representation zeta function of a FAb compactp-adic Lie group vanishes at−2.Bulletin of the London Mathematical Society, 46(2):239–244, 2014

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.817470Z

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Observation e7e4abbe-0258-40bd-8077-1056f3d812dd · outbound

This paper cites Cambridge University Press, 2002.

Vanishing of Witten zeta function at negative integers Cambridge University Press, 2002

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T14:42:45.208811Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e41b7543-4b47-47e7-b161-b9acfa7328f5 · outbound

This paper cites Number 26.

Vanishing of Witten zeta function at negative integers Number 26

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.803252Z

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Observation 44f2b6b8-6e80-4160-8c66-0d261ed0289f · outbound

This paper cites Number 29.

Vanishing of Witten zeta function at negative integers Number 29

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.796457Z

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Observation 107c6ebe-9db9-4bd0-9066-90d03f6aa00d · outbound

This paper cites Springer Science & Business Media, 2012.

Vanishing of Witten zeta function at negative integers Springer Science & Business Media, 2012

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.789735Z

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Observation aaaa8882-e619-4eb4-8265-38dd3edc24a1 · outbound

This paper cites B-functions and holonomic systems.Inventiones mathematicae, 38(1):33–53, 1976.

Vanishing of Witten zeta function at negative integers B-functions and holonomic systems.Inventiones mathematicae, 38(1):33–53, 1976

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.782745Z

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Observation 6839147e-c361-4ec0-b130-da657951a13b · outbound

This paper cites American Mathematical Soc., 2003.

Vanishing of Witten zeta function at negative integers American Mathematical Soc., 2003

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.774247Z

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Observation 93331e55-7504-4005-9a5f-b003e55b793e · outbound

This paper cites On Witten multiple zeta-functions associated with semisimple Lie algebras II.Journal of the Mathematical Society of Japan, 62(2):355–394, 2010.

Vanishing of Witten zeta function at negative integers On Witten multiple zeta-functions associated with semisimple Lie algebras II.Journal of the Mathematical Society of Japan, 62(2):355–394, 2010

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.767131Z

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Observation 4ca82d28-af85-45db-ae40-ff633055bfb9 · outbound

This paper cites On Witten multiple zeta-functions associated with semisimple Lie algebras III.Multiple Dirichlet series, L-functions and automorphic forms, pages 223–286, 2012.

Vanishing of Witten zeta function at negative integers On Witten multiple zeta-functions associated with semisimple Lie algebras III.Multiple Dirichlet series, L-functions and automorphic forms, pages 223–286, 2012

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.758693Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c453174a-1ec8-4d61-a55e-824d6fbc5183 · outbound

This paper cites On Witten multiple zeta-functions associated with semi-simple Lie algebras V.Glasgow Mathematical Journal, 57(1):107–130, 2015.

Vanishing of Witten zeta function at negative integers On Witten multiple zeta-functions associated with semi-simple Lie algebras V.Glasgow Mathematical Journal, 57(1):107–130, 2015

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.749778Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d6ebf2d0-1ed2-423a-828c-5358660d8cbc · outbound

This paper cites Zeta-functions of root systems and Poincaré poly- nomials of Weyl groups.Tohoku Mathematical Journal, Second Series, 72(1):87–126, 2020.

Vanishing of Witten zeta function at negative integers Zeta-functions of root systems and Poincaré poly- nomials of Weyl groups.Tohoku Mathematical Journal, Second Series, 72(1):87–126, 2020

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.741896Z

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Observation 019ae020-aadb-406a-8607-d21ca74d049e · outbound

This paper cites Springer, 2023.

Vanishing of Witten zeta function at negative integers Springer, 2023

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.733745Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2f7f9b69-0f7e-4ad3-a4ae-393471d3035b · outbound

This paper cites Zeros of Witten zeta functions and absolute limit.Kodai Mathematical Journal, 36(3):440–454, 2013.

Vanishing of Witten zeta function at negative integers Zeros of Witten zeta functions and absolute limit.Kodai Mathematical Journal, 36(3):440–454, 2013

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.726524Z

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Observation 83066268-7e34-4b27-b145-3551f288ccd9 · outbound

This paper cites On Witten multiple zeta-functions associated with semisimple Lie algebras I.

Vanishing of Witten zeta function at negative integers On Witten multiple zeta-functions associated with semisimple Lie algebras I

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.718741Z

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Observation ab3b3a83-2d4b-4e7f-a27c-bd444f505ec0 · outbound

This paper cites A functional relation for the Tornheim double zeta function.Acta Arithmetica, 125(3):257– 263, 2006.

Vanishing of Witten zeta function at negative integers A functional relation for the Tornheim double zeta function.Acta Arithmetica, 125(3):257– 263, 2006

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.710047Z

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Observation 47a5aa65-a567-4738-98ad-b91edc35a391 · outbound

This paper cites A functional relation for Tornheim’s double zeta functions.Acta Arithmetica, 162(4):337–354, 2014.

Vanishing of Witten zeta function at negative integers A functional relation for Tornheim’s double zeta functions.Acta Arithmetica, 162(4):337–354, 2014

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.701243Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6d3c4149-230c-42cc-a358-06ca49849740 · outbound

This paper cites On multiple Hurwitz zeta function of Mordell–Tornheim type.International Journal of Number Theory, 17(10):2327–2360, 2021.

Vanishing of Witten zeta function at negative integers On multiple Hurwitz zeta function of Mordell–Tornheim type.International Journal of Number Theory, 17(10):2327–2360, 2021

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.693103Z

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Observation 685649ca-7fef-40a3-ad67-cb31d6a31980 · outbound

This paper cites On the number ofn-dimensional representations ofSU(3), the Bernoulli numbers, and the Witten zeta function.Acta Arithmetica, 180(2):111–159, 2017.

Vanishing of Witten zeta function at negative integers On the number ofn-dimensional representations ofSU(3), the Bernoulli numbers, and the Witten zeta function.Acta Arithmetica, 180(2):111–159, 2017

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.683622Z

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Observation 9add6981-c5f0-4454-9683-94353e97896c · outbound

This paper cites Values and derivative values at nonpositive integers of generalized multiple Hurwitz zeta functions.

Vanishing of Witten zeta function at negative integers Values and derivative values at nonpositive integers of generalized multiple Hurwitz zeta functions

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-11T14:42:45.291408Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 93f0cd64-7f44-4d42-ba45-346f6a8425c5 · outbound

This paper cites an unresolved cited work.

Vanishing of Witten zeta function at negative integers Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-11T14:42:45.675805Z

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Observation 390b9222-a6bb-4ba8-adda-a633594b49ae · outbound

This paper cites On quantum gauge theories in two dimensions.Communications in Mathematical Physics, 141(1):153–209, 1991.

Vanishing of Witten zeta function at negative integers On quantum gauge theories in two dimensions.Communications in Mathematical Physics, 141(1):153–209, 1991

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.667845Z

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Observation 4dc9e074-14b3-44b1-bb35-9c8991af6f8f · outbound

This paper cites University of Cologne, Department of Mathematics and Computer Science, Weyertal 86-90, 50931 Cologne, Germany Email address:kau1@smail.uni-koeln.de.

Vanishing of Witten zeta function at negative integers University of Cologne, Department of Mathematics and Computer Science, Weyertal 86-90, 50931 Cologne, Germany Email address:kau1@smail.uni-koeln.de

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T14:42:45.657467Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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