The historical chronicle Rajatarangini, which presents a detailed account of the kings of Kashmir, was composed by:
Kalhana
Rajatarangini, a detailed chronicle of the kings of Kashmir, was composed by Kalhana in the 12th century.
Bilhana and Kshemendra were also Kashmiri Sanskrit writers, but of different works, while Somadeva is known for the Kathasaritsagara, not Rajatarangini.
Hence, Kalhana is the correct answer.
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