Quadratic forms that represent almost the same primes

Voight, John

doi:10.1090/S0025-5718-07-01976-X

Quadratic forms that represent almost the same primes
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Math. Comp. 76 (2007), 1589-1617 Request permission

Abstract:

Jagy and Kaplansky exhibited a table of $68$ pairs of positive definite binary quadratic forms that represent the same odd primes and conjectured that their list is complete outside of “trivial” pairs. In this article, we confirm their conjecture, and in fact find all pairs of such forms that represent the same primes outside of a finite set.

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