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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

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 243374, 644474, 839354, 879941, provided there require an independent check. - Hugo Pfoertner, Feb 02 2020

New title, a(1) prepended, missing term 23201 and a(29)-a(3233) from Hugo Pfoertner, Feb 02 2020

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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 243374, 644474, 839354, 879941, provided there require an independent check . - Hugo Pfoertner, Feb 02 2020

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} kroneckerKronecker(D,k)/k.

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

In Shanks's Table 5 "Hichamps, -4N = Discriminant", N = 1 is omitted , and N = 23201 is missing. After N = 24569, 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 243374, 644474, 839354, 879941, provided there require an independent check - _Hugo Pfoertner_, Feb 02 2020

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).

New title, a(1) prepended, missing term 23201 and a(29)-a(32) from Hugo Pfoertner, Feb 02 2020

Extreme values 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.

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

1,12

In Shanks's Table 5 "Hichamps, -4N = Discriminant", N = 1 is omitted and N = 23201 is missing. After N = 24569, Shanks describes the table as being tentative. 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.

Duncan A. Buell, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796 (Table 10, page 792).

Cf. A003521.

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nonn,changed,more

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