Can I make a suggestion? I found the Ohio death records for Louis (15 Jun 1948) and Martha (08 Aug 1937) Ericksen both in Canton Ohio. It lists Martha's birthdate as 03 Apr 1884 in Denmark and her parents as Peter Petersen and MaryAnn.
I found an emigration record for Marthe Kristine Pedersen from Endelave Aarhus (Endelave is apparently a small island and the records are found in Skanderborg Amt). She registered on 6-1-1904 to travel to Canton Ohio on the Hellig Olav.
I found a birth record in the parish register for Endelave, Nim, Skanderborg for a Martha Kristine Pedersen born on April 3 1884 to parents Peder Jorgensen and Mariane Mikkelsen. (I suspect that the people in Ohio were not familiar with the Danes patronymic naming system and just assumed that her father's last name would be the same as hers)
Anyway, if you think this might be the right Martha and would like copies of the records I found, just let me know.