Squarefree values of polynomial discriminants. I

DOI10.1007/s00222-022-01098-wzbMath1492.11150arXiv1611.09806OpenAlexW4210344160MaRDI QIDQ2138738

Manjul Bhargava, Xiaoheng Wang, Arul Shankar

Publication date: 12 May 2022

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09806

zbMATH Keywords

number fieldsdiscriminantsdensity of polynomials

Mathematics Subject Classification ID

Galois theory (11R32) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Class numbers, class groups, discriminants (11R29) Density theorems (11R45) Polynomials (irreducibility, etc.) (11R09)

Related Items (21)

An improvement on Schmidt’s bound on the number of number fields of bounded discriminant and small degree ⋮ A new parametrization for ideal classes in rings defined by binary forms, and applications ⋮ Rational points on hyperelliptic curves having a marked non-Weierstrass point ⋮ On the distribution of equivalence classes of random symmetric p‐adic matrices ⋮ 2-Selmer groups of even hyperelliptic curves over function fields ⋮ On the squarefree values of \(a^4+b^3\) ⋮ Heuristics for the asymptotics of the number of Sn$S_n$‐number fields ⋮ Densities on Dedekind domains, completions and Haar measure ⋮ Counting Drinfeld modules with prescribed local conditions ⋮ Two families of monogenic $S_4$ quartic number fields ⋮ Monogenic pure cubics ⋮ Odd degree number fields with odd class number ⋮ Monogenic dihedral quartic extensions ⋮ Square-free values of decomposable forms ⋮ Monogenic cyclotomic compositions ⋮ An effective Chebotarev density theorem for families of number fields, with an application to \(\ell \)-torsion in class groups ⋮ Constructing hyperelliptic curves with surjective Galois representations ⋮ On number fields with power-free discriminant ⋮ SATO–TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN -FUNCTIONS ⋮ DENSITY OF POWER‐FREE VALUES OF POLYNOMIALS ⋮ Number fields without universal quadratic forms of small rank exist in most degrees

Cites Work

• Most odd degree hyperelliptic curves have only one rational point
• On unramified Galois extensions of real quadratic number fields
• Algebraic number fields with the discriminant equal to that of a quadratic number field
• The number of extensions of a number field with fixed degree and bounded discriminant
• Bertini theorems over finite fields
• A construction of polynomials with squarefree discriminants
• COUNTING -FIELDS WITH A POWER SAVING ERROR TERM
• A positive proportion of locally soluble hyperelliptic curves over ℚ have no point over any odd degree extension
• ON THE DISTRIBUTION OF GALOIS GROUPS
• A classification of irreducible prehomogeneous vector spaces and their relative invariants
• Rational points on hyperelliptic curves having a marked non-Weierstrass point
• SATO–TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN -FUNCTIONS
• Arithmetic invariant theory
• Equality of Polynomial and Field Discriminants
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
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