Is there a DMV that shows the aggregate logical reads on a SQL server?
I think that what you might be after you may find in a different DMV:

select * from sys.dm_os_performance_counters




sys.dm_os_performance_counters

But pay attention to these features:


  Counters like Page reads/sec appear to be cumulative. Which just
  blows my poor head. In that case it should be named like 'pages read'.
  So to get actual Page reads/sec you have to do smth like:
  
  divide the counter value by amount of seconds since startup (you can
  get it by select datediff(ss,create_date, getdate()) as uptime from
  sys.databases where name = 'tempdb').