Unconditional Class Group Tabulation to 2⁴⁰ [PDF]
, 2014 In this thesis, we aim to tabulate the class groups of binary quadratic forms for all fundamental discriminants D < 0 satisfying |D| < 2⁴⁰. Our computations are performed in several stages.
Mosunov, Anton
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Missing Class Groups and Class Number Statistics for Imaginary Quadratic Fields [PDF]
, 2019 The number of imaginary quadratic fields with class number h is of classical interest: Gauss' class number problem asks for a determination of those fields counted by .
McLeman, C. +4 more
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Nonsolvable number fields ramified only at 3 and 5 [PDF]
, 2011 For p = 3 and p = 5, we exhibit a finite nonsolvable extension of Q which is ramified only at p, proving in the affirmative a conjecture of Gross.
Lassina Dembélé +5 more
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On the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields [PDF]
, 2014 Given any family of cubic fields defined by local conditions at finitely many primes, we determine the mean number of 2-torsion elements in the class groups and narrow class groups of these cubic fields, when they are ordered by their absolute ...
Manjul Bhargava +3 more
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Explicit Upper Bounds for Residues of Dedekind Zeta Functions and Values of L-Functions at s = 1, and Explicit Lower Bounds for Relative Class Numbers of CM-Fields [PDF]
, 2001 We provide the reader with a uniform approach for obtaining various useful explicit upper bounds on residues of Dedekind zeta functions of numbers fields and on absolute values of values at $s=1$ of $L$-series associated with primitive characters on ray ...
Stéphane Louboutin
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On Gauss’s class number problems [PDF]
, 1969 Let h h be the class number of binary quadratic forms (in Gauss’s formulation). All negative determinants having some h = 6 n ± 1 h = 6n \pm 1 can be determined constructively:
Daniel Shanks
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Multiplication polynomials and relative Manin-Mumford [PDF]
, 2015 After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is $(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the ...
Schmidt, Harry
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Applications of the Quaternions to the Study of Imaginary Quadratic Ring Class Groups [PDF]
, 1981 Let m = m1f2 where m1 is a square-free positive integer and m is congruent to 1 or 2 mod 4. A theorem of Gauss (see [5]) states that the number of ways to write m as a sum of 3 squares is 12 times the size of the ring class group with discriminant -4m in
Hanlon, Philip James
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, 1998 Iftis a positive integer, then a partition of a non-negative integernis at-core if none of the hook numbers of the associated Ferrers–Young diagram is a multiple oft.
Sze, Lawrence, Haglund, Jim, Ono, Ken
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On the Ono invariants of imaginary quadratic number fields [PDF]
, 2009 J. Cohen, J. Sonn, F. Sairaiji and K. Shimizu proved that there are only finitely many imaginary quadratic number fields K whose Ono invariants OnoK are equal to their class numbers hK.
Stéphane R. Louboutin +1 more
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