Bibliographic Details
| Title: |
Class fields and form class groups for solving certain quadratic Diophantine equations. |
| Authors: |
Jung, Ho Yun1 (AUTHOR) hoyunjung@dankook.ac.kr, Koo, Ja Kyung2 (AUTHOR) jkgoo@kaist.ac.kr, Shin, Dong Hwa3 (AUTHOR) dhshin@hufs.ac.kr, Yoon, Dong Sung1,4 (AUTHOR) dsyoon@pusan.ac.kr |
| Source: |
Journal of Number Theory. Oct2025, Vol. 275, p1-34. 34p. |
| Subjects: |
Congruence lattices, Modular functions, Group theory, Quadratic equations, Model theory, Quadratic fields |
| Abstract: |
Let K be an imaginary quadratic field and O be an order in K. We construct class fields associated with form class groups which are isomorphic to certain O -ideal class groups in terms of the theory of canonical models due to Shimura. As its applications, by using such class fields, for a positive integer n we first find primes of the form x 2 + n y 2 with additional conditions on x and y. Second, by utilizing these form class groups, we derive a congruence relation on special values of a modular function of higher level as an analogue of Kronecker's congruence relation. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
