Real estate such as apartment buildings or homes must be regularly maintained to remain habitable. If small plumbing, electrical, or heating and air problems are left unaddressed, then they have a way of becoming much larger issues. If you're a renter, then you may assume that any and all problems are the sole responsibility of your landlord. That's not always the case, though.
The first thing that you should do when something goes wrong in your home is to dig out the lease and read over it. You'll want to scan through the terms and conditions listed to see what they say about who's responsible for the particular concern that you're having. If it doesn't clearly address it, then you'll want to search through New York state and city laws to see what it says about it.
One reason that a particular concern may not be addressed in your lease is if local or state laws require a landlord to fix it. Most jurisdictions' laws are written to require property owners to repair any major plumbing, structural or electrical issues as these can all affect habitability.
If there's an issue that you're having that you believe your landlord should cover, then you should let them know that in writing. If they give you the go-ahead to have someone come out and make the necessary repairs, then you should send the receipt to them to reimburse you.
You may be eligible to have the housing authority step in on your behalf to compel a landlord to fix a concern if they fail to respond to your requests. You may also be able to file suit against an unresponsive landlord. A landlord/tenant matters attorney can provide you with guidance as to how to reach a strategic resolution of conflicts over residential lease agreements like yours.