\relax 
\citation{DLR}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\citation{stark1}
\citation{DLR}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Introduction}}{1}}
\citation{stevens1}
\citation{stevens2}
\citation{stevens3}
\citation{darmon-hpxh}
\citation{DD}
\citation{DP}
\citation{darmon-hpxh}
\citation{darmon-hpxh}
\citation{DLR}
\citation{DL}
\citation{CD}
\citation{DLR}
\citation{DD}
\citation{CD}
\citation{darmon-hpxh}
\citation{DL}
\citation{BDR1}
\citation{BDR2}
\citation{DR1}
\citation{DR2}
\citation{BCDDPR}
\citation{DLR}
\citation{DLR}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{The conjecture}}{2}}
\newlabel{sec:conjecture}{{1}{2}}
\citation{DLR}
\citation{DLR}
\citation{BeDi}
\citation{DLR}
\citation{DLR}
\citation{tate-book}
\citation{DasMsc}
\citation{DLR}
\citation{DLR}
\newlabel{ii}{{1}{4}}
\newlabel{lemma:dirichlet}{{1.1}{4}}
\citation{DLR}
\citation{DLR}
\citation{DS}
\citation{serre}
\newlabel{ghcus}{{2}{5}}
\newlabel{gheis}{{3}{5}}
\newlabel{matrix}{{4}{5}}
\newlabel{conj:main}{{1.2}{5}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Group-theoretic preliminaries}}{6}}
\newlabel{sec:gt-prelims}{{2}{6}}
\newlabel{eqn:decomp-central}{{5}{6}}
\newlabel{lemma:dd31}{{2.1}{6}}
\newlabel{lemma:dd22}{{2.2}{7}}
\newlabel{eqn:VhequalsVhpsi}{{6}{8}}
\newlabel{lemma:interesting-S4}{{2.3}{9}}
\citation{DR2}
\newlabel{lemma:interesting-A5}{{2.4}{10}}
\newlabel{eqn:char-A5-tilde}{{7}{10}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Circular units and Eisenstein series of weight one}}{10}}
\newlabel{sec:circular}{{3}{10}}
\newlabel{eqn:cyc-case1}{{8}{11}}
\newlabel{eqn:cyc-case2}{{9}{11}}
\newlabel{eqn:cyc-case2-bis}{{10}{11}}
\newlabel{eqn:cyc-case3}{{11}{11}}
\newlabel{eqn:cyc-case3-bis}{{12}{11}}
\newlabel{thm:cyclotomic}{{3.1}{11}}
\citation{DR1}
\newlabel{eqn:irreg-g}{{13}{12}}
\citation{BD1}
\citation{DLR}
\citation{Katz1}
\citation{gross}
\citation{de-shalit}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\newlabel{eqn:Omega-gh}{{17}{14}}
\newlabel{eqn:Omega-g}{{18}{14}}
\citation{lauder}
\newlabel{ex:eisen}{{3.3}{15}}
\citation{DLR}
\citation{de-shalit}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Elliptic units and theta series of imaginary quadratic fields}}{16}}
\newlabel{sec:elliptic}{{4}{16}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.1}{Theoretical evidence}}{16}}
\newlabel{eqn:dihedral-decomp}{{19}{16}}
\newlabel{2}{{20}{16}}
\citation{de-shalit}
\newlabel{uaa}{{21}{17}}
\newlabel{ubb}{{22}{17}}
\newlabel{eqn:caseK}{{23}{17}}
\newlabel{main-theta}{{4.1}{17}}
\newlabel{he}{{24}{17}}
\newlabel{Hecke-gh}{{25}{17}}
\citation{DLR}
\citation{BDR1}
\citation{DLR}
\citation{BDR1}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\newlabel{eq}{{26}{18}}
\newlabel{factor}{{4.2}{18}}
\newlabel{fact0}{{27}{18}}
\citation{BDR1}
\citation{DR1}
\citation{DLR}
\citation{DLR}
\newlabel{fact1}{{28}{19}}
\newlabel{le}{{4.3}{19}}
\newlabel{le-2}{{29}{19}}
\newlabel{Katz-GZ}{{30}{19}}
\citation{DLR}
\citation{DD}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Gross-Stark units and theta series of real quadratic fields}}{20}}
\newlabel{sec:gross-stark}{{5}{20}}
\newlabel{eqn:theta-psig-psih}{{31}{20}}
\citation{DLR}
\newlabel{ex:145gg}{{5.1}{21}}
\newlabel{eqn:theta-psig-eis}{{32}{21}}
\newlabel{ex-145gh}{{5.2}{22}}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Exotic forms}}{23}}
\newlabel{sec:exotic}{{6}{23}}
\newlabel{eqn:units-ad}{{33}{23}}
\newlabel{eqn:p-units-ad}{{34}{23}}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\citation{DLR}
\newlabel{eqn:adjoint-reg}{{35}{24}}
\bibcite{BCDDPR}{BCDDPR}
\bibcite{BD1}{BD2}
\bibcite{BDR1}{BDR1}
\bibcite{BDR2}{BDR2}
\bibcite{BeDi}{BeDi}
\bibcite{CD}{CD}
\bibcite{darmon-hpxh}{Dar}
\bibcite{DD}{DD}
\bibcite{de-shalit}{deS}
\bibcite{DL}{DL}
\bibcite{DLR}{DLR}
\bibcite{DP}{DP}
\bibcite{DR1}{DR1}
\bibcite{DR2}{DR2}
\bibcite{DasMsc}{Das}
\bibcite{DS}{DS}
\bibcite{gross}{Gro}
\bibcite{Katz1}{Katz1}
\bibcite{lauder}{La}
\bibcite{serre}{Se}
\bibcite{stark1}{Sta}
\bibcite{stevens1}{Ste1}
\bibcite{stevens2}{Ste2}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{26}}
\bibcite{stevens3}{Ste3}
\bibcite{tate-book}{Ta}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{13.9917pt}
\newlabel{tocindent1}{19.4667pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}