Small class numbers and extreme values of functions of quadratic fields
Author:
Duncan A. Buell
Journal:
Math. Comp. 31 (1977), 786796
MSC:
Primary 12A25; Secondary 12A30, 12A70, 1204
MathSciNet review:
0439802
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Abstract: The table of class numbers h of imaginary quadratic fields described in [1] was placed on magnetic tape. This tape was then processed to find the occurrences of and to find the successive extreme values of the Dirichlet Lfunctions , the Kronecker symbol of the field of discriminant  D. A comparison was made between the observed extrema and the bounds obtained for the Lfunctions by Littlewood [5] assuming Riemann hypotheses.
 [1]
Duncan
A. Buell, Class groups of quadratic
fields, Math. Comp. 30
(1976), no. 135, 610–623. MR 0404205
(53 #8008), http://dx.doi.org/10.1090/S0025571819760404205X
 [2]
D. SHANKS, Review of Richard B. Lakein and Sigekatu Kuroda, "Tables of class numbers for fields , ," UMT 39, Math. Comp., v. 24, 1970, pp. 491493.
 [3]
Daniel
Shanks, Systematic examination of Littlewood’s bounds on
𝐿(1,𝜒), Analytic number theory (Proc. Sympos. Pure
Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972) Amer. Math.
Soc., Providence, R.I., 1973, pp. 267–283. MR 0337827
(49 #2596)
 [4]
D.
H. Lehmer, Emma
Lehmer, and Daniel
Shanks, Integer sequences having prescribed
quadratic character, Math. Comp. 24 (1970), 433–451. MR 0271006
(42 #5889), http://dx.doi.org/10.1090/S0025571819700271006X
 [5]
J. E. LITTLEWOOD, "On the classnumber of the corpus ," Proc. London Math. Soc., v. 28, 1928, pp. 358372.
 [6]
G.
B. Mathews, Theory of numbers, 2nd ed, Chelsea Publishing Co.,
New York, 1961. MR 0126402
(23 #A3698)
 [7]
Daniel
Shanks, Calculation and applications of
Epstein zeta functions, Math. Comp. 29 (1975), 271–287.
Collection of articles dedicated to Derrick Henry Lehmer on the occasion of
his seventieth birthday. MR 0409357
(53 #13114a), http://dx.doi.org/10.1090/S00255718197504093572
 [8]
Daniel
Shanks, On Gauss’s class number
problems, Math. Comp. 23 (1969), 151–163. MR 0262204
(41 #6814), http://dx.doi.org/10.1090/S00255718196902622041
 [1]
 DUNCAN A. BUELL, "Class groups of quadratic fields," Math. Comp., v. 30, 1976, pp. 610623. MR 0404205 (53:8008)
 [2]
 D. SHANKS, Review of Richard B. Lakein and Sigekatu Kuroda, "Tables of class numbers for fields , ," UMT 39, Math. Comp., v. 24, 1970, pp. 491493.
 [3]
 DANIEL SHANKS, Systematic Examination of Littlewood's Bounds on , Proc. Sympos. Pure Math., vol. 24, Amer. Math. Soc., Providence, R.I., 1973, pp. 267283. MR 49 #2596. MR 0337827 (49:2596)
 [4]
 D. H. LEHMER, EMMA LEHMER & DANIEL SHANKS, "Integer sequences having prescribed quadratic character," Math. Comp., v. 24, 1970, pp. 433451. MR 42 #5889. MR 0271006 (42:5889)
 [5]
 J. E. LITTLEWOOD, "On the classnumber of the corpus ," Proc. London Math. Soc., v. 28, 1928, pp. 358372.
 [6]
 G. B. MATHEWS, Theory of Numbers, 2nd ed., Chelsea, New York, 1961. MR 23 #A3698. MR 0126402 (23:A3698)
 [7]
 DANIEL SHANKS, "Calculation and applications of Epstein zeta functions," Math. Comp., v. 29, 1975, pp. 271287. MR 0409357 (53:13114a)
 [8]
 DANIEL SHANKS, "On Gauss's cldass number problems," Math. Comp., v. 23, 1969, pp. 151163. MR 41 #6814. MR 0262204 (41:6814)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819770439802X
PII:
S 00255718(1977)0439802X
Article copyright:
© Copyright 1977
American Mathematical Society
