How to translate month names in “Archives”

if the translation is only for the archive widget, a filter function might work (to be added to functions.php of the theme):

add_filter('get_archives_link', 'translate_archive_month');

function translate_archive_month($list) {
  $patterns = array(
    '/January/', '/February/', '/March/', '/April/', '/May/', '/June/',
    '/July/', '/August/', '/September/', '/October/',  '/November/', '/December/'
  );
  $replacements = array(
    'jan', 'feb', 'mar', 'apr', 'may', 'jun', 
    'jul', 'aug', 'sep', 'oct', 'nov', 'dec'
  );    
  $list = preg_replace($patterns, $replacements, $list);
return $list; 
}