zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Modular forms, elliptic curves and the abc-conjecture. (English) Zbl 1046.11035
Wüstholz, Gisbert (ed.), A panorama in number theory or The view from Baker’s garden. Based on a conference in honor of Alan Baker’s 60th birthday, Zürich, Switzerland, 1999. Cambridge: Cambridge University Press (ISBN 0-521-80799-9/hbk). 128-147 (2002).
This article surveys the Masser-Oesterlé “abc” conjecture (and some of its variants) and its relations with known conjectures for elliptic curves and their moduli spaces. These latter conjectures include the Szpiro conjecture bounding the discriminant of an elliptic curve in terms of the conductor; Frey’s “degree conjecture” bounding the degree of a modular elliptic curve in terms of the conductor; the author’s “period conjecture” giving a lower bound for the periods of Frey-Hellegouarch elliptic curves in terms of the conductor; a conjectured upper bound for the size of the Tate-Shafarevich group ${\cyr Sh}$ in terms of the conductor; and the author’s “modular symbol conjecture”. For the latter two conjectures, the equivalence with abc-like conjectures is conditional on other conjectures for elliptic curves. For the entire collection see [Zbl 0997.00017].

11G05Elliptic curves over global fields
11F67Special values of automorphic $L$-series, etc