% =============================================================================
% BibTeX Bibliography for:
% "The Birch and Swinnerton-Dyer Conjecture over Finite Fields:
%  Rank, L-Functions, and the Weil Conjectures"
% Author: Rafael D. De Paz
% =============================================================================

% --- The BSD Conjecture ---

@article{BirchSwinnertonDyer1965,
  author    = {Birch, B. J. and Swinnerton-Dyer, H. P. F.},
  title     = {Notes on Elliptic Curves. {II}},
  journal   = {Journal f\"ur die reine und angewandte Mathematik},
  volume    = {218},
  pages     = {79--108},
  year      = {1965}
}

@article{Wiles2000,
  author    = {Wiles, Andrew},
  title     = {The {B}irch and {S}winnerton-{D}yer Conjecture},
  journal   = {Clay Mathematics Institute Millennium Prize Problems},
  year      = {2000},
  url       = {https://www.claymath.org/millennium/birch-and-swinnerton-dyer-conjecture/}
}

% --- Elliptic Curves and L-functions ---

@book{Silverman2009,
  author    = {Silverman, Joseph H.},
  title     = {The Arithmetic of Elliptic Curves},
  publisher = {Springer},
  series    = {Graduate Texts in Mathematics},
  volume    = {106},
  edition   = {2nd},
  year      = {2009}
}

@article{GrossZagier1986,
  author    = {Gross, Benedict H. and Zagier, Don B.},
  title     = {Heegner points and derivatives of {$L$}-series},
  journal   = {Inventiones Mathematicae},
  volume    = {84},
  number    = {2},
  pages     = {225--320},
  year      = {1986}
}

@article{Kolyvagin1989,
  author    = {Kolyvagin, V. A.},
  title     = {Finiteness of {$E(\mathbb{Q})$} and {$\text{Sha}(E, \mathbb{Q})$}
               for a subclass of {W}eil curves},
  journal   = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
  volume    = {52},
  number    = {3},
  pages     = {522--540},
  year      = {1988}
}

% --- Finite Fields, Weil Conjectures, and BSD analogue ---

@article{Tate1966,
  author    = {Tate, John},
  title     = {On the Conjectures of {B}irch and {S}winnerton-{D}yer and a Geometric Theorem},
  journal   = {S\'eminaire Bourbaki},
  volume    = {9},
  pages     = {415--440},
  year      = {1966}
}

@article{Milne1975,
  author    = {Milne, J. S.},
  title     = {On a conjecture of {A}rtin and {T}ate},
  journal   = {Annals of Mathematics},
  volume    = {102},
  number    = {3},
  pages     = {517--533},
  year      = {1975}
}

@article{Deligne1974,
  author    = {Deligne, Pierre},
  title     = {La conjecture de {W}eil. {I}},
  journal   = {Publications Math\'ematiques de l'IH\'ES},
  volume    = {43},
  pages     = {273--307},
  year      = {1974}
}

@article{KatzSarnak1999,
  author    = {Katz, Nicholas M. and Sarnak, Peter},
  title     = {Random Matrices, {F}robenius Eigenvalues, and Monodromy},
  publisher = {American Mathematical Society},
  series    = {Colloquium Publications},
  volume    = {45},
  year      = {1999}
}


@article{wiles1995modular,
  title={Modular elliptic curves and Fermat's last theorem},
  author={Wiles, Andrew},
  journal={Annals of mathematics},
  pages={443--551},
  year={1995},
  publisher={JSTOR}
}