A bound for the 3-part of class numbers of quadratic fields by means of the square sieve

DOI10.1515/FORUM.2006.034zbMath1138.11049MaRDI QIDQ3431418

Lillian Beatrix Pierce

Publication date: 10 April 2007

Published in: Forum Mathematicum (Search for Journal in Brave)

zbMATH Keywords

class numberssquare sieve

Mathematics Subject Classification ID

Quadratic extensions (11R11) Estimates on exponential sums (11L07) Applications of sieve methods (11N36) Class numbers, class groups, discriminants (11R29)

Related Items (17)

Averages and higher moments for the \(\ell\)-torsion in class groups ⋮ On \(\ell\)-torsion in class groups of number fields ⋮ A sharp upper bound for the 2‐torsion of class groups of multiquadratic fields ⋮ Geometric generalizations of the square sieve, with an application to cyclic covers ⋮ Uniform bounds for rational points on hyperelliptic fibrations ⋮ Counting problems: class groups, primes, and number fields ⋮ Counting rational points on smooth cyclic covers ⋮ An approximate form of Artin's holomorphy conjecture and non-vanishing of Artin \(L\)-functions ⋮ Burgess bounds for short character sums evaluated at forms ⋮ Imaginary quadratic fields with class group exponent 5 ⋮ Bounds for the ℓ-torsion in class groups ⋮ Diophantine equations and congruences over function fields ⋮ Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves ⋮ Missing Class Groups and Class Number Statistics for Imaginary Quadratic Fields ⋮ An effective Chebotarev density theorem for families of number fields, with an application to \(\ell \)-torsion in class groups ⋮ Average bounds for the \(\ell\)-torsion in class groups of cyclic extensions ⋮ Arithmetic exponent pairs for algebraic trace functions and applications

Cites Work

• The square sieve and consecutive square-free numbers
• The number of elliptic curves over \(\mathbb{Q}\) with conductor \(N\)
• The largest prime factor of X ³ +2
• On a question of Lillian Pierce
• The least square-free number in an arithmetic progression.
• Über die Beziehung der Klassenzahlen quadratischer Körper zueinander.
• THE 3-PART OF CLASS NUMBERS OF QUADRATIC FIELDS
• On Some Exponential Sums

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