The calculation of a large cubic class number with an application to real cyclotomic fields

Authors:
Eric Seah, Lawrence C. Washington and Hugh C. Williams

Journal:
Math. Comp. **41** (1983), 303-305

MSC:
Primary 12A50; Secondary 12-04, 12A35

DOI:
https://doi.org/10.1090/S0025-5718-1983-0701641-2

MathSciNet review:
701641

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Abstract: The class number of the cubic subfield of the *p*th cyclotomic field is calculated for the prime . This is used to construct an example where the class number of the *p*th real cyclotomic field is larger than *p*.

**[1]**G. Cornell & L. Washington, "Class numbers of cyclotomic fields,"*J. Number Theory*. (To appear.) MR**814005 (87d:11079)****[2]**K. Ireland & M. Rosen,*A Classical Introduction to Modern Number Theory*, Springer-Verlag, New York-Heidelberg-Berlin, 1982. MR**661047 (83g:12001)****[3]**C. Neild & D. Shanks, "On the 3-rank of quadratic fields and the Euler product,"*Math. Comp.*, v. 28, 1974, pp. 279-291. MR**0352042 (50:4530)****[4]**J. Oesterlé, "Versions effectives du théorème de Chebotarev sous l'hypothèse de Riemann généralisée,"*Astérisque*, v. 61, 1979, pp. 165-167.**[5]**D. Shanks, "The simplest cubic fields,"*Math. Comp.*, v. 28, 1974, pp. 1137-1152. MR**0352049 (50:4537)****[6]**H. C. Williams & J. Broere, "A computational technique for evaluating and the class number of a real quadratic field,"*Math. Comp.*, v. 30, 1976, pp. 887-893. MR**0414522 (54:2623)**

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0701641-2

Article copyright:
© Copyright 1983
American Mathematical Society