\contentsline {section}{\numberline {1}A review of Stark-Heegner points}{7}
\contentsline {subsection}{\numberline {1.1}Modular symbols}{7}
\contentsline {subsection}{\numberline {1.2}Double integrals}{9}
\contentsline {subsection}{\numberline {1.3}Indefinite integrals}{10}
\contentsline {subsection}{\numberline {1.4}Stark-Heegner points}{12}
\contentsline {section}{\numberline {2}Hida theory}{16}
\contentsline {subsection}{\numberline {2.1}Hida families}{16}
\contentsline {subsection}{\numberline {2.2}Periods attached to Hida families}{17}
\contentsline {subsection}{\numberline {2.3}Indefinite integrals revisited}{22}
\contentsline {section}{\numberline {3}$p$-adic $L$-functions }{23}
\contentsline {subsection}{\numberline {3.1}The Mazur-Kitagawa $p$-adic $L$-function}{23}
\contentsline {subsection}{\numberline {3.2}$p$-adic $L$-functions attached to real quadratic fields}{24}
\contentsline {subsection}{\numberline {3.3}A factorisation formula}{27}
\contentsline {section}{\numberline {4}Proof of the main result}{27}