Hi,

I want to change the thumbnail size for wide pictures, for example every picture with "width > 2*height", so that these thumbnails are twice the normal width.

I already tried to change this in i.php, functions-basic.php, template-functions.php and class-image.php - withouth success

Could you give me a hint where (e.g. which function) I can change this?

(I am using the "default" theme)

You should never hack core files as you will get problems with update.

You can do all this on your theme directly, there are functions for image sizes and fir width/height, there is even one to check landscape images. See the theming tutorial and the documentation.