Table of the cyclotomic class numbers ℎ*(𝑝) and their factors for 200<𝑝<521

Lehmer, D. H.; Masley, J. M.

doi:10.1090/S0025-5718-1978-0498484-2

Table of the cyclotomic class numbers $h^*(p)$ and their factors for $200<p<521$
HTML articles powered by AMS MathViewer

by D. H. Lehmer and J. M. Masley PDF

Math. Comp. 32 (1978), 577-582 Request permission

Abstract:

This table gives the values of the "first factor" ${h^\ast }(p)$ and their factorizations for all primes $p,200 < p < 521$. This extends similar data by M. Newman [Math. Comp., v. 24, 1970, pp. 215-219], and Schrutka [Berlin Akad. Abn., 1964]. The two methods used to compute these data are described.

References

L. Carlitz and F. R. Olson, Maillet’s determinant, Proc. Amer. Math. Soc. 6 (1955), 265–269. MR 69207, DOI 10.1090/S0002-9939-1955-0069207-2

J. Math. Pures Appl.

Collected Works

Timo Lepistö, On the growth of the first factor of the class number of the prime cyclotomic field, Ann. Acad. Sci. Fenn. Ser. A. I. 577 (1974), 21. MR 347772
D. H. Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. (2) 34 (1933), no. 3, 461–479. MR 1503118, DOI 10.2307/1968172
D. H. Lehmer, Prime factors of cyclotomic class numbers, Math. Comp. 31 (1977), no. 138, 599–607. MR 432589, DOI 10.1090/S0025-5718-1977-0432589-6
John Myron Masley, On the first factor of the class number of prime cyclotomic fields, J. Number Theory 10 (1978), no. 3, 273–290. MR 506638, DOI 10.1016/0022-314X(78)90024-0
Tauno Metsänkylä, On prime factors of the relative class numbers of cyclotomic fields, Ann. Univ. Turku. Ser. A I 149 (1971), 8. MR 282944
Morris Newman, A table of the first factor for prime cyclotomic fields, Math. Comp. 24 (1970), 215–219. MR 257029, DOI 10.1090/S0025-5718-1970-0257029-5
Seppo Pajunen, Computations on the growth of the first factor for prime cyclotomic fields, Nordisk Tidskr. Informationsbehandling (BIT) 16 (1976), no. 1, 85–87. MR 401706, DOI 10.1007/bf01940781
Guntram Schrutka von Rechtenstamm, Tabelle der (Relativ)-Klassenzahlen der Kreiskörper, deren $\varphi$-Funktion des Wurzelexponenten (Grad) nicht grösser als 256 ist, Abh. Deutsch. Akad. Wiss. Berlin Kl. Math. Phys. Tech. 1964 (1964), no. 2, 64 (German). MR 167646

Computers in Number Theory

Kenneth A. Ribet, A modular construction of unramified $p$-extensions of $Q(\mu _{p})$, Invent. Math. 34 (1976), no. 3, 151–162. MR 419403, DOI 10.1007/BF01403065