\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\citation{Go2}
\citation{Ri6}
\citation{Ca1}
\citation{Ho4}
\citation{Ma0}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\citation{Sh10}
\citation{Ro8}
\citation{Ka5}
\citation{Se9}
\citation{Va11}
\citation{Se9}
\citation{Gr3}
\newlabel{eq: R1}{{1}{2}{Introduction}{equation.1.1}{}}
\newlabel{eq: R2}{{2}{2}{Introduction}{equation.1.2}{}}
\newlabel{eq: R3}{{3}{2}{Introduction}{equation.1.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}The main results}{3}{section.2}}
\newlabel{eq: R4}{{4}{3}{}{equation.2.4}{}}
\newlabel{eq: R5}{{5}{3}{}{equation.2.5}{}}
\newlabel{eq: R6}{{6}{3}{}{equation.2.6}{}}
\newlabel{eq: R7}{{7}{3}{}{equation.2.7}{}}
\newlabel{eq: R8}{{8}{4}{}{equation.2.8}{}}
\newlabel{eq: R9}{{9}{4}{}{equation.2.9}{}}
\newlabel{eq: R10}{{10}{4}{}{equation.2.10}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}The preliminary results}{5}{section.3}}
\citation{Ri7}
\newlabel{eq: R11}{{11}{6}{}{equation.3.11}{}}
\newlabel{eq: R12}{{12}{6}{}{equation.3.12}{}}
\newlabel{eq: R13}{{13}{6}{}{equation.3.13}{}}
\citation{Va11}
\citation{Va11}
\newlabel{eq: R14}{{14}{7}{The preliminary results}{equation.3.14}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Additional properties of the inner sum}{8}{section.4}}
\newlabel{eq: R15}{{15}{8}{Additional properties of the inner sum}{equation.4.15}{}}
\citation{Va11}
\newlabel{eq: R16}{{16}{10}{}{equation.4.16}{}}
\citation{Va11}
\citation{Va11}
\citation{Se9}
\@writefile{toc}{\contentsline {section}{\numberline {5}The proofs of the main results}{12}{section.5}}
\newlabel{eq: R17}{{17}{12}{The proofs of the main results}{equation.5.17}{}}
\newlabel{eq: R18}{{18}{12}{The proofs of the main results}{equation.5.18}{}}
\newlabel{eq: R19}{{19}{12}{The proofs of the main results}{equation.5.19}{}}
\citation{WWW12}
\newlabel{eq: R20}{{20}{13}{The proofs of the main results}{equation.5.20}{}}
\newlabel{eq: R21}{{21}{13}{The proofs of the main results}{equation.5.21}{}}
\newlabel{eq: R22}{{22}{13}{The proofs of the main results}{equation.5.22}{}}
\newlabel{eq: R23}{{23}{14}{The proofs of the main results}{equation.5.23}{}}
\newlabel{eq: R24}{{24}{14}{The proofs of the main results}{equation.5.24}{}}
\bibcite{Ca1}{1}
\@writefile{toc}{\contentsline {section}{\numberline {6}Concluding remark}{16}{section.6}}
\bibcite{Go2}{2}
\bibcite{Gr3}{3}
\bibcite{Ho4}{4}
\bibcite{Ka5}{5}
\bibcite{Ma0}{6}
\bibcite{Ri6}{7}
\bibcite{Ri7}{8}
\bibcite{Ro8}{9}
\bibcite{Se9}{10}
\bibcite{Sh10}{11}
\bibcite{Va11}{12}
\bibcite{WWW12}{13}