Arithmetic progressions in binary quadratic forms and norm forms
نویسندگان
چکیده
منابع مشابه
Arithmetic Progressions and Binary Quadratic Forms
is a (nonconstant) arithmetic progression of positive integers. We consider a general binary quadratic form ax2 + bxy + cy' ( a , b , c E Z ) and ask the question "Can the form ax' + hxy + ry' represen1 every inleger in 1he arithmetic progression kNo + 1 for any natural numbers k and l?" In a sampling of books containing a discussion of binary quadratic forms [2]-[9], we did not find this qustl...
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has only three elements, written h(−23) = 3. There is an binary operation called composition that takes two primitive forms of the same discriminant to a third. Composition is commutative and associative, and makes the set of forms into a group, with identity 〈1, 0,−∆/4〉 for even discriminant and 〈1, 1, (1−∆)/4〉 for odd. From page 49 of Buell [1]: if a form 〈α, β, γ〉 represents a number r primi...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2019
ISSN: 0024-6093,1469-2120
DOI: 10.1112/blms.12256