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MWE

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MWE

Con el siguiente código:

\renewcommand*{\multinamedelim}{\textendash}
\renewcommand*{\finalnamedelim}{\textendash}
\DeclareCiteCommand{\citeauthor}
  {\boolfalse{citetracker}%
   \boolfalse{pagetracker}%
   \usebibmacro{prenote}}
  {\ifciteindex
     {\indexnames{labelname}}
     {}%
   \printtext[bibhyperref]{\printnames{labelname}}}
  {\multicitedelim}
  {\usebibmacro{postnote}}

  % Redefine \citeyear to only output the last two digits
\DeclareCiteCommand{\citeshortyear}
  {}
  {\bibhyperref{\printlasttwo{\thefield{year}}}}
  {\multicitedelim}
  {}

% Define a new command to print the last two digits of a string
\newcommand{\printlasttwo}[1]{\expandafter\lasttwo\StrRight{#1}{2}\relax}
\def\lasttwo#1#2\relax{#1#2\cprime}

\newcommand{\aycite}[1]{%
    {\mkbibbrackets{\citeshortyear{#1}\,\citeauthor{#1}}}%
}

Pude crear una cita similar [69' Gelfond]a \aycite{Gelfond69}, sin embargo, si la uso con citas múltiples juntas, el resultado no es el esperado: \aycite{Gelfond69,Gelfond79}->[69';79' Gelfond; Gelfond], espero [69' Gelfond; 79' Gelfond].

MWE

\documentclass{beamer}
\usepackage[bibencoding=utf8,
  backend=biber,
  style=authoryear-comp,
  doi=false,
  url=false,
  eprint=true,
  isbn=true,
  giveninits]{biblatex} 

\usepackage{xstring}
\usepackage{mathscinet}
\renewcommand*{\multinamedelim}{\textendash}
\renewcommand*{\finalnamedelim}{\textendash}

\DeclareCiteCommand{\citeauthor}
  {\boolfalse{citetracker}%
   \boolfalse{pagetracker}%
   \usebibmacro{prenote}}
  {\ifciteindex
     {\indexnames{labelname}}
     {}%
   \printtext[bibhyperref]{\printnames{labelname}}}
  {\multicitedelim}
  {\usebibmacro{postnote}}

\DeclareCiteCommand{\citeshortyear}
  {}
  {\bibhyperref{\printlasttwo{\thefield{year}}}}
  {\multicitedelim}
  {}

% Define a new command to print the last two digits of a string
\newcommand{\printlasttwo}[1]{\expandafter\lasttwo\StrRight{#1}{2}\relax}
\def\lasttwo#1#2\relax{#1#2\cprime}

\newcommand{\aycite}[1]{%
  {\mkbibbrackets{\citeshortyear{#1}\,\citeauthor{#1}}}%
}

\usepackage{filecontents}
\begin{filecontents}[overwrite]{\jobname.bib}
@incollection {Gelfond1969Hilberts,
    AUTHOR = {Gel\cprime fond, A. O.},
     TITLE = {On {H}ilbert's seventh problem},
 BOOKTITLE = {Hilbert's {P}roblems ({R}ussian)},
     PAGES = {121--127},
 PUBLISHER = {Izdat. ``Nauka'', Moscow},
      YEAR = {1969},
   MRCLASS = {10.32},
  MRNUMBER = {253994},
MRREVIEWER = {K. Mahler},
}

@incollection {Gelfond1979Hilberts,
    AUTHOR = {Gel\cprime fond, A. O.},
     TITLE = {On {H}ilbert's seventh problem},
 BOOKTITLE = {Hilbert's {P}roblems ({R}ussian)},
     PAGES = {121--127},
 PUBLISHER = {Izdat. ``Nauka'', Moscow},
      YEAR = {1979},
   MRCLASS = {10.32},
  MRNUMBER = {253994},
MRREVIEWER = {K. Mahler},
}
\end{filecontents}

\addbibresource{\jobname.bib}

\begin{document}

\aycite{Gelfond1969Hilberts,Gelfond1979Hilberts}

\printbibliography

\end{document}

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