Certain values of Hecke \(L\)-functions and generalized hypergeometric functions

DOI10.1016/j.jnt.2010.10.002zbMath1261.19004OpenAlexW2049794548MaRDI QIDQ627625

Noriyuki Otsubo

Publication date: 3 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.10.002

zbMATH Keywords

\(L\)-functiongeneralized hypergeometric functionMilnor \(K\)-groupFermat curveBeilinson conjectureregulator mapreal Deligne cohomology

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Generalized hypergeometric series, ({}_pF_q) (33C20) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27) Appell, Horn and Lauricella functions (33C65)

Related Items

The Beilinson conjectures for CM elliptic curves via hypergeometric functions ⋮ Regulators of \(K_2\) of hypergeometric fibrations ⋮ On special values at integers of \(L\)-functions of Jacobi theta products of weight 3 ⋮ On the regulator of Fermat motives and generalized hypergeometric functions ⋮ The special values of \(L\)-functions at \(s=1\) of theta products of weight 3 ⋮ Product formulas for hypergeometric functions over finite fields ⋮ On Special Values of Jacobi-Sum HeckeL-Functions

Cites Work

• On the periods of Abelian integrals and a formula of Chowla and Selberg. With an appendix by David E. Rohrlich
• Higher regulators and values of \(L\)-functions
• Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
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• \(K_ 2\) of a Fermat quotient and the value of its \(L\)-function
• On the regulator of Fermat motives and generalized hypergeometric functions
• Higher Regulators, Algebraic 𝐾-Theory, and Zeta Functions of Elliptic Curves
• Jacobi Sums as "Grossencharaktere"
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