The research of the first author was supported by Natural Sciences and Engineering Research Council Canada Grant No. A-7233, while that of the second was supported by a Natural Sciences and Engineering Research Council Canada Undergraduate Summer Research Award.The research of the first author was supported by Natural Sciences and Engineering Research Council Canada Grant No. A-7233, while that of the second was supported by a Natural Sciences and Engineering Research Council Canada Undergraduate Summer Research Award.https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/class-numbers-and-biquadratic-reciprocity/00FECEE10C8CB10943F2ED8E7AAE2B8
AbstractWe address a question posed by Ono [Ken Ono, The Web of Modularity: Arithmetic of the Coeffi...
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AbstractCongruence conditions on the class numbers of complex quadratic fields have recently been st...
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AbstractCongruences for the Apéry numbers are proved which generalize the results and conjectures of...
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AbstractWe address a question posed by Ono [Ken Ono, The Web of Modularity: Arithmetic of the Coeffi...
AbstractLet p be an odd prime and n an integer relatively prime to p. In this work three criteria wh...
AbstractLet p ≡ ± 1 (mod 8) be a prime which is a quadratic residue modulo 7. Then p = M2 + 7N2, and...
AbstractA congruence modulo 8 is proved relating the class numbers of the quadratic fields Q(√p) and...
AbstractLet h(d) denote the class number of the quadratic field Q(√d) of discriminant d. A number of...
AbstractLet Q(−k) be an imaginary quadratic field with discriminant −k and class number h, with k≠3,...
AbstractLet d, d1, d2 ϵ N be square free with d=d1d2, and let h(-d) and IK denote the class number a...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in ...
AbstractWe prove a congruence modulo a certain power of 2 for the class numbers of the quadratic fie...
AbstractFor an odd prime p, let l(p) denote the least positive prime which is a quadratic residue mo...
AbstractLet q and p be prime with q = a2 + b2 ≡ 1 (mod 4), a ≡ 1 (mod 4), and p = qf + 1. In the nin...
AbstractCongruence conditions on the class numbers of complex quadratic fields have recently been st...
AbstractThis paper presents a general congruence modulo a certain power of 2 relating the class numb...
AbstractCongruences for the Apéry numbers are proved which generalize the results and conjectures of...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
AbstractWe address a question posed by Ono [Ken Ono, The Web of Modularity: Arithmetic of the Coeffi...
AbstractLet p be an odd prime and n an integer relatively prime to p. In this work three criteria wh...
AbstractLet p ≡ ± 1 (mod 8) be a prime which is a quadratic residue modulo 7. Then p = M2 + 7N2, and...