% Bibliography for thakur-conjectures.tex.
% Verification (2026-10-23, by the AI coordinator): arXiv entries checked
% against the arXiv API (title, authors, first-version date); journal data
% checked against Crossref metadata or the publisher page.  Entries whose
% existence could not be confirmed carry "unverified" in the note field.

@article{Thakur2009PowerSums,
  author  = {Thakur, Dinesh S.},
  title   = {Power sums with applications to multizeta and zeta zero distribution for {$\mathbb{F}_q[t]$}},
  journal = {Finite Fields Appl.},
  volume  = {15},
  year    = {2009},
  number  = {4},
  pages   = {534--552},
  doi     = {10.1016/j.ffa.2009.04.002},
}

@article{Thakur2013Vadic,
  author  = {Thakur, Dinesh S.},
  title   = {Valuations of $v$-adic power sums and zero distribution for the {Goss} $v$-adic zeta function for {$\mathbb{F}_q[t]$}},
  journal = {J. Integer Seq.},
  volume  = {16},
  year    = {2013},
  number  = {2},
  pages   = {Article 13.2.13},
  url     = {https://cs.uwaterloo.ca/journals/JIS/VOL16/Thakur/thakur5.html},
  note    = {Author version consulted: \url{https://archive.math.arizona.edu/thakur/powerfinal.pdf}},
}

@article{Thakur2009Relations,
  author  = {Thakur, Dinesh S.},
  title   = {Relations between multizeta values for {$\mathbb{F}_q[t]$}},
  journal = {Int. Math. Res. Not. IMRN},
  year    = {2009},
  number  = {12},
  pages   = {2318--2346},
  doi     = {10.1093/imrn/rnp018},
}

@article{Thakur2010Shuffle,
  author  = {Thakur, Dinesh S.},
  title   = {Shuffle relations for function field multizeta values},
  journal = {Int. Math. Res. Not. IMRN},
  year    = {2010},
  doi     = {10.1093/imrn/rnp202},
  note    = {Issue and pages not verified (Crossref lists online date 2009-12-07 only)},
}

@book{Thakur2004Book,
  author    = {Thakur, Dinesh S.},
  title     = {Function Field Arithmetic},
  publisher = {World Scientific},
  address   = {River Edge, NJ},
  year      = {2004},
}

@misc{ThakurCRM,
  author = {Thakur, Dinesh S.},
  title  = {Arithmetic of gamma, zeta and multizeta values for function fields},
  note   = {Notes of a CRM Barcelona advanced course (2010), \url{https://www.sas.rochester.edu/mth/sites/dinesh-thakur/crmDec12.pdf} (retrieved 2026-10-23)},
}

@article{ThakurPAMQ,
  author  = {Thakur, Dinesh S.},
  title   = {Recent progress and open problems in function field arithmetic---the influence of {John Tate}'s work},
  journal = {Pure Appl. Math. Q.},
  volume  = {6},
  year    = {2010},
  number  = {1},
  pages   = {1--20},
  note    = {Author PDF \url{https://www.sas.rochester.edu/mth/sites/dinesh-thakur/PAMQtate.pdf} (retrieved 2026-10-23; title and pages from its first page)},
}

@misc{ChenOno2026,
  author        = {Chen, Evan and Ono, Ken},
  title         = {Thakur's hypotheses on power sums of {$\mathbb{F}_q[t]$}},
  year          = {2026},
  eprint        = {2606.16239},
  archivePrefix = {arXiv},
  note          = {Preprint, arXiv:2606.16239v1},
}

@article{LRT14,
  author  = {Lara Rodr{\'\i}guez, Jos{\'e} Alejandro and Thakur, Dinesh S.},
  title   = {Zeta-like multizeta values for {$\mathbb{F}_q[t]$}},
  journal = {Indian J. Pure Appl. Math.},
  volume  = {45},
  year    = {2014},
  number  = {5},
  pages   = {787--801},
  doi     = {10.1007/s13226-014-0089-0},
  note    = {arXiv:1312.4928},
}

@article{LRT20,
  author  = {Lara Rodr{\'\i}guez, Jos{\'e} Alejandro and Thakur, Dinesh S.},
  title   = {Zeta-like multizeta values for higher genus curves},
  journal = {J. Th\'eor. Nombres Bordeaux},
  volume  = {33},
  year    = {2021},
  number  = {2},
  pages   = {553--581},
  doi     = {10.5802/jtnb.1169},
  note    = {arXiv:2003.12910},
}

@article{CNP23,
  author  = {Chung, Kwun and Ngo Dac, Tuan and Pellarin, Federico},
  title   = {Universal families of {Eulerian} multiple zeta values in positive characteristic},
  journal = {Adv. Math.},
  volume  = {422},
  year    = {2023},
  pages   = {Paper No. 109003},
  doi     = {10.1016/j.aim.2023.109003},
  note    = {arXiv:2111.06973},
}

@article{CPY19,
  author  = {Chang, Chieh-Yu and Papanikolas, Matthew A. and Yu, Jing},
  title   = {An effective criterion for {Eulerian} multizeta values in positive characteristic},
  journal = {J. Eur. Math. Soc. (JEMS)},
  volume  = {21},
  year    = {2019},
  number  = {2},
  pages   = {405--440},
  doi     = {10.4171/JEMS/840},
  note    = {arXiv:1411.0124},
}

@article{LeNgoDac22,
  author  = {Le, Huy Hung and Ngo Dac, Tuan},
  title   = {Zeta-like multiple zeta values in positive characteristic},
  journal = {Math. Z.},
  volume  = {301},
  year    = {2022},
  number  = {2},
  pages   = {2037--2057},
  doi     = {10.1007/s00209-022-02970-4},
  note    = {HAL: hal-03093398},
}

@article{Chen17,
  author  = {Chen, Huei-Jeng},
  title   = {Anderson--{Thakur} polynomials and multizeta values in positive characteristic},
  journal = {Asian J. Math.},
  volume  = {21},
  year    = {2017},
  number  = {6},
  pages   = {1135--1152},
  doi     = {10.4310/AJM.2017.v21.n6.a6},
  note    = {arXiv:1506.06463},
}

@article{KuanLin16,
  author  = {Kuan, Yen-Liang and Lin, Yi-Hsuan},
  title   = {Criterion for deciding zeta-like multizeta values in positive characteristic},
  journal = {Exp. Math.},
  volume  = {25},
  year    = {2016},
  number  = {3},
  pages   = {246--256},
  doi     = {10.1080/10586458.2015.1069228},
}

@article{ChenKuan18,
  author  = {Chen, Huei-Jeng and Kuan, Yen-Liang},
  title   = {On depth 2 zeta-like families},
  journal = {J. Number Theory},
  volume  = {184},
  year    = {2018},
  pages   = {411--427},
  doi     = {10.1016/j.jnt.2017.08.027},
}

@article{Chang14,
  author  = {Chang, Chieh-Yu},
  title   = {Linear independence of monomials of multizeta values in positive characteristic},
  journal = {Compos. Math.},
  volume  = {150},
  year    = {2014},
  number  = {11},
  pages   = {1789--1808},
  doi     = {10.1112/S0010437X1400743X},
  note    = {arXiv:1207.2326},
}

@article{CCM23,
  author  = {Chang, Chieh-Yu and Chen, Yen-Tsung and Mishiba, Yoshinori},
  title   = {On {Thakur}'s basis conjecture for multiple zeta values in positive characteristic},
  journal = {Forum Math. Pi},
  volume  = {11},
  year    = {2023},
  pages   = {Paper No. e26},
  doi     = {10.1017/fmp.2023.26},
  note    = {arXiv:2205.09929},
}

@article{IKLNDP24,
  author  = {Im, Bo-Hae and Kim, Hojin and Le, Khac Nhuan and Ngo Dac, Tuan and Pham, Lan Huong},
  title   = {Zagier--{Hoffman}'s conjectures in positive characteristic},
  journal = {Forum Math. Pi},
  volume  = {12},
  year    = {2024},
  pages   = {Paper No. e18},
  doi     = {10.1017/fmp.2024.18},
  note    = {arXiv:2205.07165},
}

@article{NgoDac21,
  author  = {Ngo Dac, Tuan},
  title   = {On {Zagier}--{Hoffman}'s conjectures in positive characteristic},
  journal = {Ann. of Math. (2)},
  volume  = {194},
  year    = {2021},
  number  = {1},
  pages   = {361--392},
  doi     = {10.4007/annals.2021.194.1.6},
}

@article{Todd18,
  author  = {Todd, George},
  title   = {A conjectural characterization for {$\mathbb{F}_q(t)$}-linear relations between multizeta values},
  journal = {J. Number Theory},
  volume  = {187},
  year    = {2018},
  pages   = {264--287},
  doi     = {10.1016/j.jnt.2017.09.028},
}

@misc{Hu26,
  author        = {Hu, Jinyuan},
  title         = {Todd's relation conjecture and binary relations for multiple zeta values in positive characteristic},
  year          = {2026},
  eprint        = {2609.08263},
  archivePrefix = {arXiv},
  note          = {Preprint, arXiv:2609.08263v2; not refereed},
}

@misc{KMU23,
  author        = {Kramer-Miller, Joe and Upton, James},
  title         = {Zeros of the {Goss} zeta function},
  year          = {2023},
  eprint        = {2312.01264},
  archivePrefix = {arXiv},
  note          = {Preprint, arXiv:2312.01264v1},
}

@article{Sheats98,
  author  = {Sheats, Jeffrey T.},
  title   = {The {Riemann} hypothesis for the {Goss} zeta function for {$\mathbb{F}_q[T]$}},
  journal = {J. Number Theory},
  volume  = {71},
  year    = {1998},
  number  = {1},
  pages   = {121--157},
  doi     = {10.1006/jnth.1998.2232},
}

@article{Goss00,
  author  = {Goss, David},
  title   = {A {Riemann} hypothesis for characteristic $p$ {$L$}-functions},
  journal = {J. Number Theory},
  volume  = {82},
  year    = {2000},
  number  = {2},
  pages   = {299--322},
  note    = {arXiv:math/9907019},
}

@misc{DVPC14,
  author        = {Diaz-Vargas, Javier and Polanco-Chi, Enrique},
  title         = {{Riemann} hypothesis for {Goss} $t$-adic zeta function},
  year          = {2014},
  eprint        = {1408.1111},
  archivePrefix = {arXiv},
  note          = {Preprint, arXiv:1408.1111v1},
}

@article{WenYao02,
  author  = {Wen, Zhi-Ying and Yao, Jia-Yan},
  title   = {Transcendence, automata theory and gamma functions for polynomial rings},
  journal = {Acta Arith.},
  volume  = {101},
  year    = {2002},
  number  = {1},
  pages   = {39--51},
  doi     = {10.4064/aa101-1-3},
}

@article{MFY97,
  author  = {Mend{\`e}s France, Michel and Yao, Jia-Yan},
  title   = {Transcendence and the {Carlitz}--{Goss} gamma function},
  journal = {J. Number Theory},
  volume  = {63},
  year    = {1997},
  number  = {2},
  pages   = {396--402},
  doi     = {10.1006/jnth.1997.2104},
}

@article{CKMFR80,
  author  = {Christol, Gilles and Kamae, Teturo and Mend{\`e}s France, Michel and Rauzy, G{\'e}rard},
  title   = {Suites alg{\'e}briques, automates et substitutions},
  journal = {Bull. Soc. Math. France},
  volume  = {108},
  year    = {1980},
  number  = {4},
  pages   = {401--419},
  doi     = {10.24033/bsmf.1926},
}

@article{Yu91,
  author  = {Yu, Jing},
  title   = {Transcendence and special zeta values in characteristic $p$},
  journal = {Ann. of Math. (2)},
  volume  = {134},
  year    = {1991},
  number  = {1},
  pages   = {1--23},
  doi     = {10.2307/2944331},
}

@article{CPTY10,
  author  = {Chang, Chieh-Yu and Papanikolas, Matthew A. and Thakur, Dinesh S. and Yu, Jing},
  title   = {Algebraic independence of arithmetic gamma values and {Carlitz} zeta values},
  journal = {Adv. Math.},
  volume  = {223},
  year    = {2010},
  number  = {4},
  pages   = {1137--1154},
  doi     = {10.1016/j.aim.2009.09.013},
}

@article{ABP04,
  author  = {Anderson, Greg W. and Brownawell, W. Dale and Papanikolas, Matthew A.},
  title   = {Determination of the algebraic relations among special {$\Gamma$}-values in positive characteristic},
  journal = {Ann. of Math. (2)},
  volume  = {160},
  year    = {2004},
  number  = {1},
  pages   = {237--313},
  doi     = {10.4007/annals.2004.160.237},
}

@article{CM19,
  author  = {Chang, Chieh-Yu and Mishiba, Yoshinori},
  title   = {On multiple polylogarithms in characteristic $p$: $v$-adic vanishing versus $\infty$-adic {Eulerianness}},
  journal = {Int. Math. Res. Not. IMRN},
  year    = {2019},
  number  = {3},
  pages   = {923--947},
  doi     = {10.1093/imrn/rnx151},
  note    = {arXiv:1511.03490},
}

@article{CM21,
  author  = {Chang, Chieh-Yu and Mishiba, Yoshinori},
  title   = {On a conjecture of {Furusho} over function fields},
  journal = {Invent. Math.},
  volume  = {223},
  year    = {2021},
  number  = {1},
  pages   = {49--102},
  doi     = {10.1007/s00222-020-00988-1},
}

@article{Chen25,
  author  = {Chen, Yen-Tsung},
  title   = {A $v$-adic variant of {Anderson}--{Brownawell}--{Papanikolas} linear independence criterion and its application},
  journal = {Math. Res. Lett.},
  volume  = {32},
  year    = {2025},
  number  = {4},
  pages   = {1085--1120},
  doi     = {10.4310/MRL.251123230910},
  note    = {arXiv:2308.05825},
}

@misc{CWY24,
  author        = {Chang, Chieh-Yu and Wei, Fu-Tsun and Yu, Jing},
  title         = {$v$-adic periods of {Carlitz} motives and {Chowla}--{Selberg} formula revisited},
  year          = {2024},
  eprint        = {2407.15024},
  archivePrefix = {arXiv},
  note          = {Preprint, arXiv:2407.15024v3},
}

@misc{Chang25Gauss,
  author        = {Chang, Ting-Wei},
  title         = {Geometric {Gauss} sums and {Gross}--{Koblitz} formula over function fields},
  year          = {2025},
  eprint        = {2502.01109},
  archivePrefix = {arXiv},
}

@misc{SageMath,
  author = {{The Sage Developers}},
  title  = {{SageMath}, the {Sage} {Mathematics} {Software} {System} ({V}ersion 10.8)},
  year   = {2025},
  note   = {\url{https://www.sagemath.org}},
}

@misc{ClaudeCode,
  author = {{Anthropic}},
  title  = {Claude Code},
  year   = {2026},
  note   = {Agentic coding tool; model \texttt{claude-opus-5-5}. \url{https://claude.com/claude-code}},
}

@misc{Mathcity,
  author = {Dupuy, Taylor},
  title  = {mathcity: skills for mathematical research agents},
  note   = {\url{https://github.com/tdupu/mathcity}; public availability not established by the authoring agent},
}

% AI-generated research records harvested by this paper (directories of the
% repository github.com/tdupu/dumps, which may be private).
@misc{DataPS,
  author = {{AI research record}},
  title  = {Thakur's power-sum hypotheses {H1}, {H2} for non-prime $q$},
  year   = {2026},
  note   = {Directory \texttt{ai/2026-10-23-thakur-power-sum-h1-h2-nonprime/} of \url{https://github.com/tdupu/dumps}; AI-generated (Claude Code, claude-opus-5-5), not human-reviewed},
}
@misc{DataZL,
  author = {{AI research record}},
  title  = {Zeta-like {MZVs} over {$\mathbb{F}_q[t]$}: status of the characterization conjectures},
  year   = {2026},
  note   = {Directory \texttt{ai/2026-10-23-thakur-zeta-like-mzv-characterization/} of \url{https://github.com/tdupu/dumps}; AI-generated, not human-reviewed},
}
@misc{DataHG,
  author = {{AI research record}},
  title  = {{Lara Rodr\'iguez}--{Thakur} higher-genus zeta-like conjectures: status},
  year   = {2026},
  note   = {Directory \texttt{ai/2026-10-23-thakur-higher-genus-zeta-like/} of \url{https://github.com/tdupu/dumps}; AI-generated, not human-reviewed},
}
@misc{DataMZ,
  author = {{AI research record}},
  title  = {Are all relations among {$\mathbb{F}_q[t]$} multizeta values consequences of shuffle relations?},
  year   = {2026},
  note   = {Directory \texttt{ai/2026-10-23-thakur-mzv-relations-shuffle-only/} of \url{https://github.com/tdupu/dumps}; AI-generated, not human-reviewed},
}
@misc{DataGZ,
  author = {{AI research record}},
  title  = {Thakur's conjectures on zeros of {Goss} zeta functions for general {$A$}},
  year   = {2026},
  note   = {Directory \texttt{ai/2026-10-23-thakur-goss-zeta-zeros-general-A/} of \url{https://github.com/tdupu/dumps}; AI-generated, not human-reviewed},
}
@misc{DataAT,
  author = {{AI research record}},
  title  = {Thakur's automata and transcendence questions for function-field special values},
  year   = {2026},
  note   = {Directory \texttt{ai/2026-10-23-thakur-automata-transcendence/} of \url{https://github.com/tdupu/dumps}; AI-generated, not human-reviewed},
}
@misc{Checks,
  author = {{AI coordinator}},
  title  = {Independent checks for this paper},
  year   = {2026},
  note   = {Directory \texttt{latex/thakur-conjectures/harvest/checks/} of \url{https://github.com/tdupu/dumps}; scripts and outputs written by the AI agent that assembled this paper},
}