If you submit an objection by e-mail, you cannot later prove whether and when the message reached the tax office. If it is important to meet deadlines, you should send by registered post or fax instead.
A signature is therefore not a mandatory requirement. § 87a para. 1 sentence 1 AO also permits the transmission of electronic documents, provided the recipient has opened access for this purpose. If an e-mail address is provided on the tax assessment notice, this indicates the tax office's willingness to receive electronically.