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Small class numbers and extreme values of L-functions of quadratic fields. (English) Zbl 0379.12001


MSC:

11R11 Quadratic extensions
11R23 Iwasawa theory
11M35 Hurwitz and Lerch zeta functions
12-04 Software, source code, etc. for problems pertaining to field theory
11R42 Zeta functions and \(L\)-functions of number fields
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Online Encyclopedia of Integer Sequences:

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.
Values of m in the discriminant D = -4*m leading to a new minimum of the L-function of the Dirichlet series L(1) = Sum_{k>=1} Kronecker(D,k)/k.
Largest squarefree number k such that Q(sqrt(-k)) has class number n.
Discriminants of imaginary quadratic fields with class number 5 (negated).
Discriminants of imaginary quadratic fields with class number 6 (negated).
Discriminants of imaginary quadratic fields with class number 7 (negated).
Discriminants of imaginary quadratic fields with class number 8 (negated).
Discriminants of imaginary quadratic fields with class number 9 (negated).
Discriminants of imaginary quadratic fields with class number 10 (negated).
Discriminants of imaginary quadratic fields with class number 11 (negated).
Discriminants of imaginary quadratic fields with class number 12 (negated).
Discriminants of imaginary quadratic fields with class number 13 (negated).
Discriminants of imaginary quadratic fields with class number 14 (negated).
Discriminants of imaginary quadratic fields with class number 15 (negated).
Discriminants of imaginary quadratic fields with class number 16 (negated).
Discriminants of imaginary quadratic fields with class number 17 (negated).
Discriminants of imaginary quadratic fields with class number 18 (negated).
Discriminants of imaginary quadratic fields with class number 19 (negated).
Discriminants of imaginary quadratic fields with class number 21 (negated).
Discriminants of imaginary quadratic fields with class number 23 (negated).
Number of negative fundamental discriminants having class number n.
Smallest squarefree integer k such that Q(sqrt(-k)) has class number n, or 0 if no such k exists.
Class number, k, of n, i.e.; imaginary quadratic fields negated Q(sqrt(-n))=k, or 0 if n is not a fundamental discriminant (A003657).