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.**30**(1976), no. 135, 610–623. MR**0404205**, https://doi.org/10.1090/S0025-5718-1976-0404205-X**[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 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****[4]**D. H. Lehmer, Emma Lehmer, and Daniel Shanks,*Integer sequences having prescribed quadratic character*, Math. Comp.**24**(1970), 433–451. MR**0271006**, https://doi.org/10.1090/S0025-5718-1970-0271006-X**[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 Publishing Co., New York, 1961. MR**0126402****[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**, https://doi.org/10.1090/S0025-5718-1975-0409357-2**[8]**Daniel Shanks,*On Gauss’s class number problems*, Math. Comp.**23**(1969), 151–163. MR**0262204**, https://doi.org/10.1090/S0025-5718-1969-0262204-1

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Additional Information

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

Article copyright:
© Copyright 1977
American Mathematical Society