The arithmetic of function fields. II: The 'cyclotomic' theory

DOI10.1016/0021-8693(83)90212-0zbMath0516.12010OpenAlexW2058796915MaRDI QIDQ1052397

David Goss

Publication date: 1983

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(83)90212-0

zbMATH Keywords

class groupsBernoulli numberscyclotomic fieldsDrinfeld modulesBernoulli polynomialscyclotomic unitIwasawa main conjectureStickelberger theoremelliptic modular formsArtin L-series for curvesclass group of curvecurve over finite fieldelliptic modulesLanglands conjecture for function fieldsp-adic L-seriesspecial values of zeta-functiontwo-variable L-seriesWeil conjecturezeta function for curves

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Units and factorization (11R27) (zeta (s)) and (L(s, chi)) (11M06) Arithmetic ground fields for curves (14H25) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Class field theory (11R37) Zeta functions and (L)-functions of number fields (11R42) Cyclotomic extensions (11R18) Algebraic numbers; rings of algebraic integers (11R04) Zeta functions and (L)-functions (11S40) Formal groups, (p)-divisible groups (14L05) Langlands-Weil conjectures, nonabelian class field theory (11R39) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Algebraic functions and function fields in algebraic geometry (14H05) Arithmetic problems in algebraic geometry; Diophantine geometry (14G99)

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Cites Work

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