Learn Finnish: En ole kuullut kuulumisia viikkoihin. - I haven't heard any news for weeks.

In negative sentences, Finnish uses the illative case to express how long something hasn't happened. Here, viikkoihin (the plural illative of viikko) translates to 'for weeks'. If the sentence were positive, you would use a different time expression, but negative duration always triggers the illative.

How does kuulumisia relate to the verb kuullut?

They share the same root! Kuulumisia is the partitive plural of kuulumiset, which means 'news' or 'tidings' (often used when asking someone how they are doing). It comes from the verb kuulua (to be heard). So literally, you are saying you haven't heard 'the things to be heard'.

Why must kuulumisia be in the partitive case?

Because the main action is negative (en ole kuullut). In Finnish, the object of a negative sentence is always put in the partitive case. Even if the sentence were positive, 'news' is an undefined amount here, which would also normally trigger the partitive.

Could I just say 'en kuullut' instead of 'en ole kuullut'?

You could, but it changes the meaning. Just like in English, the perfect tense (en ole kuullut / I haven't heard) shows that this lack of news started in the past and continues right up to the present moment. If you used the basic past tense (en kuullut / I didn't hear), it would refer to a specific, finished event in the past.