A conjectural characterization for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-linear relations between multizeta values

Todd, George

doi:10.1016/j.jnt.2017.09.028

Cited by 11 publications

(27 citation statements)

References 9 publications

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“…of weight 3, (working for all d, or equivalently working for the corresponding F-functions), in contrast to the existence of such "binary" relations [26]. We have also checked that the same situation persists, even if we add S d+2 (1, 2), S d−1 (3), S d+2 (3), but have not tried adding more terms.…”

Section: Some Remarks (I) Explicit F-functions In Standard Formsmentioning

confidence: 92%

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Zeta-like Multizeta Values for higher genus curves

Rodríguez¹,

Thakur

2021

Journal De Théorie Des Nombres De Bordeaux

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Section: Some Remarks (I) Explicit F-functions In Standard Formsmentioning

confidence: 92%

“…, again in contrast to the genus zero situation [26]. (See also [25, p. 17-18] for relevant discussion of Todd's data.…”

Section: Some Remarks (I) Explicit F-functions In Standard Formsmentioning

confidence: 99%

Zeta-like Multizeta Values for higher genus curves

Rodríguez¹,

Thakur

2021

Journal De Théorie Des Nombres De Bordeaux

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“…In this section we investigate linear relations for MZV's. Our approach is based on techniques dealing with power sums studied by Thakur [25] and crucial operations introduced by Todd [28].…”

Section: Algebraic Toolsmentioning

confidence: 99%

“…Then Todd [28] defined the B * maps and the C maps between the previous sets of binary relations as follows.…”

Section: Algebraic Toolsmentioning

confidence: 99%

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On Zagier-Hoffman's conjectures in positive characteristic

Dac

2021

Ann. of Math. (2)

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We study Todd-Thakur's analogues of Zagier-Hoffman's conjectures in positive characteristic. These conjectures predict the dimension and an explicit basis Tw of the span of characteristic p multiple zeta values of fixed weight w which were introduced by Thakur as analogues of classical multiple zeta values of Euler.In the present paper we first establish the algebraic part of these conjectures which states that the span of characteristic p multiple zeta values of weight w is generated by the set Tw. As a consequence, we obtain upper bounds for the dimension. This is the analogue of Brown's theorem and also those of Deligne-Goncharov and Terasoma.We then prove two results towards the transcendental part of these conjectures. First, we establish the linear independence for a large subset of Tw and yield lower bounds for the dimension. Second, for small weights we prove the linear independence for the whole set Tw and completely solve Zagier-Hoffman's conjectures in positive characteristic. Our key tool is the Anderson-Brownawell-Papanikolas criterion for linear independence in positive characteristic.

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Zeta-like multiple zeta values in positive characteristic

Dac

2022

Math. Z.

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We study multiple zeta values (MZV's) over the rational function field over Fq which were introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we affirmatively solve a conjecture of Lara Rodriguez and Thakur which gives a full list of zeta-like MZV's of weight at most q 2 and depth 2. Further, we completely determine all zeta-like MZV's of weight at most q 2 and arbitrary depth. Our method is based on a criterion which is derived from the Anderson-Thakur motivic interpretation of MZV's and the Anderson-Brownawell-Papanikolas criterion for linear independence in positive characteristic.

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A conjectural characterization for Fq(t)-linear relations between multizeta values

Cited by 11 publications

References 9 publications

Zeta-like Multizeta Values for higher genus curves

Zeta-like Multizeta Values for higher genus curves

On Zagier-Hoffman's conjectures in positive characteristic

Zeta-like multiple zeta values in positive characteristic

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