Hilbert 12: cubic divisor development

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

Read the typeset paper

1 \begin{thebibliography}{99}
2 \bibitem{BCG} N.~Bergeron, P.~Charollois and L.~E.~Garc\'ia,
3 \emph{Elliptic units for complex cubic fields (On Eisenstein's Jugendtraum)}.
4 Checked primary authors' 44-page PDF, \url{https://webusers.imj-prg.fr/~pierre.charollois/BCG_cubic.pdf}.
5 The source checkpoints identify arXiv:2311.04110v2; this edition's literature verification authenticates the authors' copy and its controlling formulas, rather than silently identifying its bytes with the inaccessible v2 artifact. Product/continuation conventions, Theorem~3.2 and the fixed example in Section~5.2 are the controlling uses.
6 \bibitem{Milne} J.~S.~Milne, \emph{Class Field Theory}, version~4.03, August~6, 2020. Cubic reciprocity and Artin induction in Chapter~VIII. \url{https://www.jmilne.org/math/CourseNotes/CFTc.pdf}.
7 \bibitem{Cogdell} J.~W.~Cogdell, \emph{On Artin $L$-functions}, author's PDF, Section~2.2, local inertia-invariant Euler factors and induction compatibility. \url{https://math.osu.edu/~cogdell/artin-www.pdf}.
8 \bibitem{Sutherland} A.~V.~Sutherland, \emph{18.785 Lecture~19: The analytic class number formula}, November~15, 2016. Residue formula and completed zeta functional equation. MIT course notes. \url{https://math.mit.edu/classes/18.785/2016fa/LectureNotes19.pdf}.
9 \bibitem{DLMFTheta} NIST Digital Library of Mathematical Functions, Section~21.2: multidimensional theta definition and Gaussian-scaled bound. \url{https://dlmf.nist.gov/21.2}.
10 \bibitem{DLMFProducts} NIST Digital Library of Mathematical Functions, Section~1.10: analytic infinite products and termwise logarithmic differentiation. \url{https://dlmf.nist.gov/1.10}.
11 \bibitem{DLMFWeierstrass} NIST Digital Library of Mathematical Functions, Sections~23.6 and~23.10: Weierstrass sigma--theta relation and addition identities; in particular Equation~23.10.3. \url{https://dlmf.nist.gov/23.10.E3}.
12 \bibitem{Jensen} T.~Tao, \emph{246B Notes~1: Zeroes, poles, and factorisation of meromorphic functions}, December~23, 2020. Jensen formula and finite-growth zero bounds. \url{https://terrytao.wordpress.com/2020/12/23/246b-notes-1-zeroes-poles-and-factorisation-of-meromorphic-functions/}.
13 \bibitem{DLMFSine} NIST Digital Library of Mathematical Functions, Section~4.22: infinite products and partial fractions for trigonometric functions. \url{https://dlmf.nist.gov/4.22}.
14 \end{thebibliography}

Back to source controls

Back to Hilbert 12: cubic divisor development