Determination of the algebraic relations among special Γ-values in positive characteristic

By Greg W. Anderson, W. Brownawell, Matthew A. Papanikolas. 2002

154 citations recorded by the source corpus.

We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values of the geometric r-function over F q [T] are explained by the standard functional equations.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bfc5bf25d8d68bd5acd4e10ac6c8b31dc80db59a

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Determination of algebraic relations among special zeta values in positive characteristic (2007, methodology): “We follow Papanikolas [5] (cf. also [ 2 ]) in working with t-motives.”
Tannakian duality for Anderson–Drinfeld motives and algebraic independence of Carlitz logarithms (2005, methodology): “on [11, Prop. II.2.21(b)]. Thus πM is an isomorphism of aﬃne group schemes over Fq(t). 6. Galoisgroups and transcendence In this section we ﬁrst recall the linear independence criterion introduced in [2] by Anderson, Brownawell, and the author, and one of its applications to t-motives. We then link ”
Multizeta values for F_q[t], their period interpretation and relations between them (2009, methodology): “ﬁnition of multizeta sums come up naturally as entries in triangular matrices satisfying shtuka F− 1 equations. The original t-motive formalism [A86] or the equivalent dual t-motive formalism used in [ABP04] will then realize these matrices as period matrices of appropriate iterated extensions of te”
Arithmetic of positive characteristic $L$-series values in Tate algebras (2014, result): “K (see the work of Chieh-Yu Chang and Jing Yu [10], where they use the Tannaka approach introduced by Papanikolas in [17] and the algebraic independence theory of Anderson, Brownawell, Papanikolas in [1]). This result is accessible due to a result of Anderson and Thakur [4, Theorem 3.8.3] implying t”
Linear independence of monomials of multizeta values in positive characteristic (2012, methodology): “ute the dimension of the Galois group in question at this moment. 4 CHIEH-YU CHANG The overall strategy of showing Theorem 3.4.4 is to use the criterion established by Anderson-Brownawell-Papanikolas [ABP04] (abbreviated as ABP-criterion). We apply the ABP-criterion to lift the given k¯-linear relat”
Universal Gauss-Thakur sums and $$L$$L-series (2013, background): “For instance, the function = 1 (t − θ)ω entire, determines a rigid analytic trivialization of the Carlitz (dual) t-motive (following Anderson, Brownawell and Papanikolas in [3]).”