Algebraic independence of values of Goss \(L\)-functions at \(s=1\)

DOI10.1016/j.jnt.2012.04.002zbMath1328.11082arXiv1105.6341OpenAlexW2963335685WikidataQ60118124 ScholiaQ60118124MaRDI QIDQ1932392

Brad A. Lutes, Matthew A. Papanikolas

Publication date: 18 January 2013

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.6341

zbMATH Keywords

special valuesalgebraic independencespecial polynomialsGoss \(L\)-functionsDrinfeld logarithms

Mathematics Subject Classification ID

Drinfel'd modules; higher-dimensional motives, etc. (11G09) Transcendence theory of Drinfel'd and (t)-modules (11J93) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items (5)

Values of certain \(L\)-series in positive characteristic ⋮ Algebraic relations among Goss’s zeta values on elliptic curves ⋮ A note on special values of 𝐿-functions ⋮ Tensor powers of rank 1 Drinfeld modules and periods ⋮ Special \(L\)-values and shtuka functions for Drinfeld modules on elliptic curves

Cites Work

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• Analytic homomorphisms into Drinfeld modules
• Anderson's root numbers and Thakur's Gauss sums
• Shtukas and Jacobi sums
• Log-algebraicity of twisted \(A\)-harmonic series and special values of \(L\)-series in characteristic \(p\)
• Study of \(L(s,\chi)/\pi^s\) for \(L\)-functions relative to \(\mathbb{F}_q((T^{-1}))\) and associated to characters of degree 1
• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• Transcendental values of class group $L$-functions, II
• Algebraic independence of periods and logarithms of Drinfeld modules

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