Geodesic
Class Number Divisibility in Real Quadratic Function Fields
Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 361-370

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Let q be a positive power of an odd prime p, and let Fq(t) be the function field with coefficients in the finite field of q elements. Let denote the ideal class number of the real quadratic function field obtained by adjoining the square root of an even-degree monic . The following theorem is proved: Let n ≧ 1 be an integer not divisible by p. Then there exist infinitely many monic, squarefree polynomials, such that n divides the class number, . The proof constructs an element of order n in the ideal class group.
DOI : 10.4153/CMB-1992-048-5
Mots-clés : 11A55, 11R29, Continued Fractions, Function Fields, Class Numbers 
Friesen, Christian. Class Number Divisibility in Real Quadratic Function Fields. Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 361-370. doi: 10.4153/CMB-1992-048-5
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     title = {Class {Number} {Divisibility} in {Real} {Quadratic} {Function} {Fields}},
     journal = {Canadian mathematical bulletin},
     pages = {361--370},
     year = {1992},
     volume = {35},
     number = {3},
     doi = {10.4153/CMB-1992-048-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-048-5/}
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