\contentsline {section}{\tocsection {}{}{Introduction}}{1}
\contentsline {section}{\tocsection {}{1}{Overconvergent weight one forms and Gross-Stark units}}{11}
\contentsline {subsection}{\tocsubsection {}{1.1}{Classical and overconvergent modular forms of weight one}}{11}
\contentsline {subsection}{\tocsubsection {}{1.2}{The Gross-Stark unit attached to a weight one form}}{14}
\contentsline {subsubsection}{\tocsubsubsection {}{1.2.1}{The case where $\varrho _g$ is irreducible}}{14}
\contentsline {subsubsection}{\tocsubsubsection {}{1.2.2}{The case where $\varrho _g$ is reducible}}{16}
\contentsline {section}{\tocsection {}{2}{Iterated integrals and the Garrett-Hida $p$-adic $L$-function}}{17}
\contentsline {section}{\tocsection {}{3}{Heegner points and theta series of imaginary quadratic fields}}{23}
\contentsline {subsection}{\tocsubsection {}{3.1}{Heegner points and elliptic units}}{24}
\contentsline {subsection}{\tocsubsection {}{3.2}{Conjecture $\shi $ when $p$ splits in $K$}}{26}
\contentsline {subsection}{\tocsubsection {}{3.3}{Numerical evidence for inert primes}}{33}
\contentsline {subsubsection}{\tocsubsubsection {}{3.3.1}{General remarks}}{33}
\contentsline {subsubsection}{\tocsubsubsection {}{3.3.2}{Numerical evidence}}{35}
\contentsline {section}{\tocsection {}{4}{Stark-Heegner points and theta series of real quadratic fields}}{40}
\contentsline {subsection}{\tocsubsection {}{}{4.1\hspace {1em}{Theoretical preliminaries}}}{40}
\contentsline {subsection}{\tocsubsection {}{4.2}{Numerical evidence}}{41}
\contentsline {section}{\tocsection {}{5}{Stark points over $A_4$, $S_4$ or $A_5$ extensions and exotic weight one forms}}{46}
\contentsline {subsection}{\tocsubsection {}{5.1}{Theoretical preliminaries}}{46}
\contentsline {subsubsection}{\tocsubsubsection {}{5.1.1}{Cases where $g$ is of tetrahedral type}}{47}
\contentsline {subsubsection}{\tocsubsubsection {}{5.1.2}{Cases where $g$ is of octahedral type}}{48}
\contentsline {subsubsection}{\tocsubsubsection {}{5.1.3}{Cases where $g$ is of icosahedral type}}{49}
\contentsline {subsection}{\tocsubsection {}{5.2}{Numerical evidence}}{50}
\contentsline {section}{\tocsection {}{6}{Stark points attached to odd two-dimensional Artin representations}}{56}
\contentsline {section}{\tocsection {}{7}{Stark points over cyclotomic fields and Eisenstein series}}{57}
\contentsline {subsection}{\tocsubsection {}{7.1}{Theoretical preliminaries}}{57}
\contentsline {subsection}{\tocsubsection {}{7.2}{Numerical evidence}}{59}
\contentsline {section}{\tocsection {Appendix}{A}{Digest of numerical examples}}{61}
\contentsline {section}{\tocsection {}{}{References}}{62}