Concept

Ankeny–Artin–Chowla congruence

Summary
In number theory, the Ankeny–Artin–Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla. It concerns the class number h of a real quadratic field of discriminant d > 0. If the fundamental unit of the field is :\varepsilon = \frac{t + u \sqrt{d}}{2} with integers t and u, it expresses in another form :\frac{ht}{u} \pmod{p}; for any prime number p > 2 that divides d. In case p > 3 it states that :-2{mht \over u} \equiv \sum_{0 < k < d} {\chi(k) \over k}\lfloor {k/p} \rfloor \pmod {p} where m = \frac{d}{p};   and  \chi;  is the Dirichlet character for the quadratic field. For p = 3 there is a factor (1 + m) multiplying the LHS. Here :\lfloor x\rfloor represents the floor function of x. A related result is that if d=p is congruent to one mod four, then :{u \over t}h \equiv
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading