Congruences for odd class numbers of quadratic fields with odd discriminant
J Kim, Y Mizuno - The Ramanujan Journal, 2023 - Springer
For any distinct two primes p 1≡ p 2≡ 3 (mod 4), let h (-p 1), h (-p 2) and h (p 1 p 2) be the
class numbers of the quadratic fields Q (-p 1), Q (-p 2) and Q (p 1 p 2), respectively. Let ω p 1 …
class numbers of the quadratic fields Q (-p 1), Q (-p 2) and Q (p 1 p 2), respectively. Let ω p 1 …
Congruences relating class numbers of quadratic orders and Zagier's sums
Y Mizuno - Journal of Number Theory, 2021 - Elsevier
We prove a congruence modulo 16 relating the class numbers h (− 4 p), h (16 p) of quadratic
orders and Zagier's sum m (4 p) associated to 4 p, when p≡ 1 (mod 4) is a prime. This gives …
orders and Zagier's sum m (4 p) associated to 4 p, when p≡ 1 (mod 4) is a prime. This gives …
Some congruences connecting quadratic class numbers with continued fractions
W Cheng, X Guo - Acta Arithmetica, 2019 - impan.pl
Let $ p $ be a prime number, and $ h (-p) $ and $ h (p) $ be the ideal class numbers of the
quadratic fields $\mathbb {Q}(\sqrt {-p}) $ and $\mathbb {Q}(\sqrt {p}) $ respectively. We …
quadratic fields $\mathbb {Q}(\sqrt {-p}) $ and $\mathbb {Q}(\sqrt {p}) $ respectively. We …
Congruences on the class numbers of for a prime
J Kim, Y Mizuno - arXiv preprint arXiv:2210.02668, 2022 - arxiv.org
For a prime $ p\equiv 3$$(\text {mod} 4) $, let $ h (-8p) $ and $ h (8p) $ be the class numbers
of $\mathbb {Q}(\sqrt {-2p}) $ and $\mathbb {Q}(\sqrt {2p}) $, respectively. Let $\Psi (\xi) $ be …
of $\mathbb {Q}(\sqrt {-2p}) $ and $\mathbb {Q}(\sqrt {2p}) $, respectively. Let $\Psi (\xi) $ be …