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A003420 Values of m in the discriminant D = -4*m leading to a new maximum of the L-function of the Dirichlet series L(1) = Sum_{k=1..oo} Kronecker(D,k)/k.
(Formerly M1387)
4
1, 2, 5, 11, 14, 26, 41, 89, 101, 194, 314, 341, 689, 1091, 1154, 1889, 2141, 3449, 3506, 5561, 6254, 8126, 8774, 10709, 13166, 15461, 23201, 24569, 30014, 81149, 81626, 162686, 243374 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In Shanks's Table 5 "Hichamps, -4N = Discriminant", N = 1 is omitted, and N = 23201 is missing. Shanks describes the table as being tentative after N = 24569. In Buell's Table 10 "Successive maxima of L(1) for even discriminants", the values N = 11 and N = 1091 are missing in the D/4 column. The further terms 644474, 839354, 879941, provided there require an independent check. - Hugo Pfoertner, Feb 02 2020

REFERENCES

D. Shanks, Systematic examination of Littlewood's bounds on L(1,chi), pp. 267-283 of Analytic Number Theory, ed. H. G. Diamond, Proc. Sympos. Pure Math., 24 (1973). Amer. Math. Soc.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..33.

Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796 (Table 10, page 792).

D. Shanks, Systematic examination of Littlewood's bounds on L(1,chi), Proc. Sympos. Pure Math., 24 (1973). Amer. Math. Soc. (Annotated scanned copy)

EXAMPLE

a(1) = 1: L(1) for D=-4*1 ~= 0.785398... = Pi/4.

a(2) = 2: L(1) for D=-4*2 ~= 1.11072073... = Pi/(2*sqrt(2)), a(2) > a(1);

L(1) for D=-4*3 ~= 0.90689..., L(1) for D=-4*4 ~= 0.785398..., both < a(2);

a(3) = 5: L(1) for D=-4*5 = 1.40496..., a(3) > a(2).

CROSSREFS

Cf. A003521.

Sequence in context: A287708 A026228 A331949 * A206602 A338013 A336190

Adjacent sequences:  A003417 A003418 A003419 * A003421 A003422 A003423

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

New title, a(1) prepended, missing term 23201 and a(29)-a(33) from Hugo Pfoertner, Feb 02 2020

STATUS

approved

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Last modified April 15 01:01 EDT 2021. Contains 342971 sequences. (Running on oeis4.)