Hecke Operator and Pellian Equation Conjecture

Hongwen Lu
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Hongwen Lu: University of Science and Technology of China, Department of Mathematics

A chapter in International Symposium in Memory of Hua Loo Keng, 1991, pp 183-191 from Springer

Abstract: Abstract Let the prime p ≡ 3 (mod 4). In this note, we prove an identity relating Hecke operator to the conjecture that the least solution for Pellian equation x 2−py 2= 1 satisfies p ∤ u. We also find that the conjecture is a consequence of a conjecture on the Hecke operator.

Date: 1991
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DOI: 10.1007/978-3-662-07981-2_9

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