The Riemann hypothesis in characteristic \(p\) in historical perspective

DOI10.1007/978-3-319-99067-5zbMath1414.11003OpenAlexW2894099048MaRDI QIDQ1668479

Peter Roquette

Publication date: 28 August 2018

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-99067-5

zbMATH Keywords

Riemann hypothesisglobal function fieldsHelmut HasseAndré WeilFriedrich Karl SchmidtMax Deuringzeta function in characteristic \(p\), Emil Artin

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) History of mathematics in the 20th century (01A60) Research exposition (monographs, survey articles) pertaining to number theory (11-02) History of number theory (11-03) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) History of algebraic geometry (14-03) Sociology (and profession) of mathematics (01A80) Algebraic functions and function fields in algebraic geometry (14H05)

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Higher reciprocity law and an analogue of the Grunwald-Wang theorem for the ring of polynomials over an ultra-finite field ⋮ Artin's primitive root conjecture for function fields revisited ⋮ On the Hasse invariants of the Tate normal forms \(E_5\) and \(E_7\) ⋮ Sums of Powers in Large Finite Fields: A Mix of Methods ⋮ Lorenzen and Constructive Mathematics

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