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dc.contributor.author
Kazalicki, Matija
dc.contributor.author
Kohen, Daniel
dc.date.available
2018-08-15T11:15:22Z
dc.date.issued
2017-12
dc.identifier.citation
Kazalicki, Matija; Kohen, Daniel; Supersingular zeros of divisor polynomials of elliptic curves of prime conductor; Springer; Research in Mathematical Sciences; 4; 10; 12-2017; 1-17
dc.identifier.issn
2197-9847
dc.identifier.uri
http://hdl.handle.net/11336/55559
dc.description.abstract
For a prime number p, we study the zeros modulo p of divisor polynomials of rational elliptic curves E of conductor p. Ono (CBMS regional conference series in mathematics, 2003, vol 102, p. 118) made the observation that these zeros are often j-invariants of supersingular elliptic curves over Fp¯. We show that these supersingular zeros are in bijection with zeros modulo p of an associated quaternionic modular form vE. This allows us to prove that if the root number of E is - 1 then all supersingular j-invariants of elliptic curves defined over Fp are zeros of the corresponding divisor polynomial. If the root number is 1, we study the discrepancy between rank 0 and higher rank elliptic curves, as in the latter case the amount of supersingular zeros in Fp seems to be larger. In order to partially explain this phenomenon, we conjecture that when E has positive rank the values of the coefficients of vE corresponding to supersingular elliptic curves defined over Fp are even. We prove this conjecture in the case when the discriminant of E is positive, and obtain several other results that are of independent interest.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Brandt Module
dc.subject
Divisor Polynomial
dc.subject
Supersingular Elliptic Curves
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Supersingular zeros of divisor polynomials of elliptic curves of prime conductor
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-08-14T14:00:54Z
dc.journal.volume
4
dc.journal.number
10
dc.journal.pagination
1-17
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Kazalicki, Matija. University of Zagreb; Croacia
dc.description.fil
Fil: Kohen, Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
dc.journal.title
Research in Mathematical Sciences
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://resmathsci.springeropen.com/articles/10.1186/s40687-017-0099-8
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1186/s40687-017-0099-8
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