Small class numbers and extreme values of -functions of quadratic fields

Author:
Duncan A. Buell

Journal:
Math. Comp. **31** (1977), 786-796

MSC:
Primary 12A25; Secondary 12A30, 12A70, 12-04

DOI:
https://doi.org/10.1090/S0025-5718-1977-0439802-X

MathSciNet review:
0439802

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Abstract | References | Similar Articles | Additional Information

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 *L*-functions , the Kronecker symbol of the field of discriminant - *D*. A comparison was made between the observed extrema and the bounds obtained for the *L*-functions by Littlewood [5] assuming Riemann hypotheses.

**[1]**DUNCAN A. BUELL, "Class groups of quadratic fields,"*Math. Comp.*, v. 30, 1976, pp. 610-623. 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. 491-493.**[3]**DANIEL SHANKS,*Systematic Examination of Littlewood's Bounds on*, Proc. Sympos. Pure Math., vol. 24, Amer. Math. Soc., Providence, R.I., 1973, pp. 267-283. 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. 433-451. MR**42**#5889. MR**0271006 (42:5889)****[5]**J. E. LITTLEWOOD, "On the class-number of the corpus ,"*Proc. London Math. Soc.*, v. 28, 1928, pp. 358-372.**[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. 271-287. MR**0409357 (53:13114a)****[8]**DANIEL SHANKS, "On Gauss's cldass number problems,"*Math. Comp.*, v. 23, 1969, pp. 151-163. MR**41**#6814. MR**0262204 (41:6814)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0439802-X

Article copyright:
© Copyright 1977
American Mathematical Society