That's the most well-known witch-process in DK.
Christian IV was along with James I very keen on hunting witches.
IMO not because they were bad, sadists or fanatics. They were certainly not poorly-educated either!
But both kings were devout Christians who genuinely believed that bad and evil things happened because of the Devil and his allies and it was their duty as kings to protect their countries and people against witches and the Devil and his demons.
Christian IV certainly, despite being one of the most famous, celebrated and enterprising kings in Danish history was also the most eager witch-hunter.
However, under his successor, Frederik III, witch-hunting de facto ended in Denmark.
The last official witch-burning in DK took place in early 1700's. There may have been local lynchings, but that is unclear.
Christian IV and James I knew each other personally. Partly because Christian IV's sister was married to James I, but also because Christian IV went on an official state visit to England.
You can read about it here:
And they discussed the witch-issue certainly during that visit and probably in letters as well.
The majority of people who were burned in Protestant Europe were women. (In Catholic Europe they burned heretics instead and they were mainly men). However, men were also burned as sorcerers. And sometimes animals. There are acts from trials in modern-day Germany of animals who were sentenced to be burned because they were thought to be possessed by the Devil.
You can read another version of this witch-trial, translated and commented by me: https://app.box.com/s/f895wqf005hy68acez3z0dw59pwd9ag3