SHA512withRSA - Looking for details about the Signature Algorithm I am trying to find information about the Signature Algorithm SHA512withRSA and have been unsuccessful so far.

In the current state, the signature is too long, so I would like to check the code for overhead and try to remove reduce the size.

Can anybody give me some pointers on how to achieve that.
References

Related to your reference request: SHA512withRSA points to the RSA Signature Scheme with Appendix based on PKCS #1 v1.5 with SHA-512 hash function.

This means you’re looking for reference documentation describing RSA PKCS1 v1.5 (see: RFC2313) signatures with SHA512 (see: RFC6234) hash and X.509 encoding format.

Removing “overhead” from code

As for the part of your question on how to achieve the removal of overhead in your code: diving into that could quickly become off-topic for Crypto.SE and it would probably be more suitable for StackOverflow anyway. Nevertheless – since your question indicates you’re new to the reference documentations and RFCs describing SHA2, RSA, etc. – I would like to add my two cents to your code-modification idea…

Cryptographic implementations rarely contain or produce (what you call) “overhead”. Therefore, I would like to strongly discourage you from stripping or modifying any part of code that represents, interacts, or relates to cryptographical algorithms or schemes. Doing so has a high probability of introducing issues – which might range from simple software bugs, up to a dangerous situation where the removal of code is equal to the voiding (= removal) of cryptographic security. You surely don’t want the later to happen. Instead of fiddling with the code, you should simply rely a tested and well-vetted implementation. There are many of them out there, available in almost every programming language you could wish for.