Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data

Download original file

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

Read the typeset paper

1 \providecommand{\OO}{\mathcal O}
2 \providecommand{\FF}{\mathbb F}\providecommand{\QQ}{\mathbb Q}\providecommand{\ZZ}{\mathbb Z}\providecommand{\RR}{\mathbb R}
3 \providecommand{\Spec}{\operatorname{Spec}}\providecommand{\Supp}{\operatorname{Supp}}\providecommand{\Fitt}{\operatorname{Fitt}}
4 \providecommand{\Ann}{\operatorname{Ann}}\providecommand{\coker}{\operatorname{coker}}\providecommand{\im}{\operatorname{im}}
5 \providecommand{\rank}{\operatorname{rank}}\providecommand{\Tr}{\operatorname{Tr}}\providecommand{\id}{\operatorname{id}}
6 \providecommand{\whot}{\mathbin{\widehat\otimes}}\providecommand{\m}{\mathfrak m}\providecommand{\p}{\mathfrak p}
7 \providecommand{\head}[1]{\par\vspace{2pt}{\sffamily\bfseries\fontsize{10}{12}\selectfont #1}\par\vspace{1pt}}
8 \providecommand{\platecaption}[1]{\par\noindent{\footnotesize\color{black!70}#1\par}}
9 \newtcolorbox{insight}{colback=accent!3,colframe=accent,boxrule=0pt,leftrule=1.1pt,arc=0pt,left=10pt,right=10pt,top=5pt,bottom=5pt,fontupper=\fontsize{10}{12}\selectfont,before skip=6pt,after skip=5pt}
10 \providecommand{\takeaway}[1]{\begin{insight}\textbf{Read this as:}\ #1\end{insight}}
11 \providecommand{\vfig}[2][.92]{\par\begingroup\centering\resizebox{#1\linewidth}{!}{\input{visual_graphics/#2.tex}}\par\endgroup\vspace{2pt}}
12 
13 \newif\ifstarted\startedfalse
14 \providecommand{\vpage}[4]{\ifstarted\clearpage\else\startedtrue\fi
15 \pdfbookmark[1]{V#1. #2}{plate#1}\hypertarget{vpage#1}{}\label{visual:#1}
16 {\sffamily\fontsize{9}{11}\selectfont\bfseries\color{accent}V#1\quad /\quad #3\par}\vspace{5pt}
17 {\sffamily\bfseries\fontsize{19}{22}\selectfont #2\par}\vspace{5pt}
18 {\sffamily\fontsize{8.7}{11}\selectfont\color{muted} #4\par}\vspace{6pt}}
19 \providecommand{\pagerefV}[1]{\hyperlink{vpage#1}{V\,--\,#1}}
20 
21 \providecommand{\CC}{\mathbb C}
22 \providecommand{\kk}{\mathbb k}
23 \renewcommand{\AA}{\mathcal A}
24 \providecommand{\BB}{\mathcal B}
25 \providecommand{\Hull}{\operatorname{Hull}}
26 \providecommand{\srank}{\operatorname{srank}}
27 \providecommand{\Span}{\operatorname{span}}
28 \providecommand{\End}{\operatorname{End}}
29 \providecommand{\diag}{\operatorname{diag}}
30 \providecommand{\Ker}{\operatorname{ker}}
31 \providecommand{\norm}[1]{\left\lVert#1\right\rVert}
32 \providecommand{\mat}[1]{\begin{pmatrix}#1\end{pmatrix}}
33 
34 \providecommand{\Ob}{\operatorname{Ob}}
35 \providecommand{\supp}{\operatorname{supp}}
36 \providecommand{\src}{\operatorname{src}}\providecommand{\tgt}{\operatorname{tgt}}
37 
38 
39 \providecommand{\captiontext}[1]{\platecaption{#1}}

Back to source controls

Back to Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data