Besides that the Messiah must be of Davidic lineage, must he also be the greatest torah scholar of the generation (of Davidic lineage)?
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Rambam in Melachim 11:7 says that he will be "הוגה בתורה ועוסק במצוות כדויד אביו", roughly one who learns Torah and does mitzvos like David his father, but does not seem to require him to be the greatest Torah scholar of the generation. In fact in Melachim 11:6 he mentions the fact that Rabbi Akiva thought that Bar Kochba was going to be the Messiah, when we don't have any record of Bar Kochba being the greatest Torah scholar of his generation, and presumably there were other great scholars of Davidic decent alive at the time, such as the descendants of the house of Hillel who served as the Nassi of the Sanhedrin.