\contentsline {section}{\tocsection {}{1}{Introduction}}{1}
\contentsline {section}{\tocsection {}{2}{Complex $L$-series}}{2}
\contentsline {subsection}{\tocsubsection {}{2.1}{Eisenstein series}}{3}
\contentsline {subsection}{\tocsubsection {}{2.2}{Rankin's method}}{4}
\contentsline {subsection}{\tocsubsection {}{2.3}{A factorisation of critical values}}{6}
\contentsline {subsection}{\tocsubsection {}{2.4}{Beilinson's formula}}{7}
\contentsline {subsection}{\tocsubsection {}{2.5}{Algebraicity}}{8}
\contentsline {section}{\tocsection {}{3}{$p$-adic $L$-functions}}{9}
\contentsline {subsection}{\tocsubsection {}{3.1}{Rankin's $p$-adic $L$-functions}}{9}
\contentsline {subsection}{\tocsubsection {}{3.2}{Factorisation of $p$-adic $L$-functions}}{10}
\contentsline {section}{\tocsection {}{4}{$p$-adic regulators}}{11}
\contentsline {subsection}{\tocsubsection {}{4.1}{The regulator on $K_2$}}{12}
\contentsline {subsection}{\tocsubsection {}{4.2}{The general case}}{14}
\contentsline {section}{\tocsection {}{5}{The $p$-adic Beilinson formula}}{15}
\contentsline {subsection}{\tocsubsection {}{5.1}{The main results}}{15}
\contentsline {subsection}{\tocsubsection {}{5.2}{Relation with the work of Brunault and Gealy}}{15}
\contentsline {section}{\tocsection {}{}{References}}{17}