thesis.bib

% !TEX root = Daniel-Miller-thesis.tex

@article{akiyama-tanigawa-1999,
	author  = {Akiyama, Shigeki and Tanigawa, Yoshio},
	title   = {Calculation of values of {$L$}-functions associated to elliptic curves},
	journal = {Math. Comp.},
	volume  = {68},
	year    = {1999},
	number  = {227},
	pages   = {1201--1231}
}

@book{apostol-1976,
	author    = {Apostol, Tom},
	title     = {Introduction to analytic number theory},
	note      = {Undergraduate Texts in Mathematics},
	publisher = {Springer-Verlag, New York-Heidelberg},
	year      = {1976}
}

@article{arnold-krylov-1963,
	author  = {Arnol'd, Vladimir and Krylov, Alexander},
	title   = {Uniform distribution of points on a sphere and certain ergodic properties of solutions of linear ordinary differential equations in a complex domain},
	journal = {Dokl. Akad. Nauk SSSR},
	volume  = {148},
	year    = {1963},
	pages   = {9--12}
}

@article{bght-2011,
	author  = {Barnet-Lamb, Tom and Geraghty, David and Harris, Michael and Taylor, Richard},
	title   = {A family of {C}alabi-{Y}au varieties and potential automorphy {II}},
	journal = {Publ. Res. Inst. Math. Sci.},
	volume  = {47},
	year    = {2011},
	number  = {1},
	pages   = {29--98}
}

@incollection{bockle-2013,
	author    = {B\"ockle, Gebhard},
	title     = {Deformations of {G}alois representations},
	booktitle = {Elliptic curves, {H}ilbert modular forms and {G}alois deformations},
	series    = {Adv. Courses Math. CRM Barcelona},
	pages     = {21--115},
	publisher = {Birkh\"auser/Springer, Basel},
	year      = {2013}
}

@book{bourbaki-2005,
	author    = {Bourbaki, Nicolas},
	title     = {Lie groups and {L}ie algebras. {C}hapters 7--9},
	series    = {Elements of Mathematics (Berlin)},
	note      = {Translated from the 1975 and 1982 French originals by Andrew Pressley},
	publisher = {Springer-Verlag, Berlin},
	year      = {2005},
	pages     = {xii+434}
}

@article{breuillard-gelander-2003,
	author  = {Breuillard, Emmanuel and Gelander, Tsachik},
	title   = {On dense free subgroups of {L}ie groups},
	journal = {J. Algebra},
	volume  = {261},
	year    = {2003},
	number  = {2},
	pages   = {448--467}
}

@misc{bucar-kedlaya-2015,
	author = {Bucar, Alina and Kedlaya, Kiran},
	title  = {An application of the effective {S}ato--{T}ate conjecture},
	year   = {2015},
	note   = {arXiv:1301.0139}
}

@book{bugeaud--2012,
	author    = {Bugeaud, Yann},
	title     = {Distribution modulo one and {D}iophantine approximation},
	series    = {Cambridge Tracts in Mathematics},
	volume    = {193},
	publisher = {Cambridge University Press, Cambridge},
	year      = {2012}
}

@article{clozel-harris-taylor-2008,
	author  = {Clozel, Laurent and Harris, Michael and Taylor, Richard},
	title   = {Automorphy for some {$l$}-adic lifts of automorphic mod {$l$} {G}alois representations},
	journal = {Publ. Math. Inst. Hautes \'Etudes Sci.},
	number  = {108},
	year    = {2008},
	pages   = {1--181} 
}

@article{doob-1949,
	author  = {Doob, Joseph},
	title   = {Heuristic approach to the {K}olmogorov--{S}mirnov theorems},
	journal = {Ann. Math. Statistics},
	volume  = {20},
	year    = {1949},
	pages   = {393--403}
}

@book{drmota-tichy-1997,
	author    = {Drmota, Michael and Tichy, Robert},
	title     = {Sequences, discrepancies and applications},
	series    = {Lecture Notes in Mathematics},
	volume    = {1651},
	publisher = {Springer-Verlag, Berlin},
	year      = {1997}
}

@book{edwards-1974,
	author    = {Edwards, Harold},
	title     = {Riemann's zeta function},
	series    = {Pure and Applied Mathematics},
	volume    = {58},
	publisher = {Academic Press},
	year      = {1974}
}

@book{folland-1999,
	author    = {Folland, Gerald},
	title     = {Real analysis},
	series    = {Pure and Applied Mathematics},
	edition   = {Second},
	publisher = {John Wiley \& Sons},
	year      = {1999}
}

@incollection{harris-2009,
	author    = {Harris, Michael},
	title     = {Potential automorphy of odd-dimensional symmetric powers of elliptic curves and applications},
	booktitle = {Algebra, arithmetic, and geometry: in honor of {Y}u. {I}. {M}anin. {V}ol. {II}},
	series    = {Progr. Math.},
	volume    = {270},
	pages     = {1--21},
	publisher = {Birkh\"auser Boston},
	year      = {2009}
}

@article{harris-shepherd-barron-taylor-2010,
	author  = {Harris, Michael and Shepherd-Barron, Nick and Taylor, Richard},
	title   = {A family of {C}alabi-{Y}au varieties and potential automorphy},
	journal = {Ann. of Math. (2)},
	volume  = {171},
	year    = {2010},
	number  = {2},
	pages   = {779--813}
}

@article{jarnik-1936,
	author  = {Jarn\'{i}k, Vojt\v{e}ch},
	title   = {{\"U}ber eien {S}atz von {A}. {K}hintchine. {Z}weite {M}itteilung},
	journal = {Acta Arith.},
	volume  = {2},
	year    = {1936},
	number  = {1},
	pages   = {1--22}
}

@book{katz-1988,
	author    = {Katz, Nicholas},
	title     = {Gauss sums, {K}loosterman sums, and monodromy groups},
	series    = {Annals of Mathematics Studies},
	volume    = {116},
	publisher = {Princeton University Press, Princeton, NJ},
	year      = {1988}
}

@article{khare-larsen-ramakrishna-2005,
	author  = {Khare, Chandrashekhar and Larsen, Michael and Ramakrishna, Ravi},
	title   = {Constructing semisimple {$p$}-adic {G}alois representations with prescribed properties},
	journal = {Amer. J. Math.},
	volume  = {127},
	year    = {2005},
	number  = {4},
	pages   = {709--734}
}

@article{khare-rajan-2001,
	author  = {Khare, Chandrashekhar and Rajan, Conjeeveram},
	title   = {The density of ramified primes in semisimple {$p$}-adic {G}alois representations},
	journal = {Internat. Math. Res. Notices},
	year    = {2001},
	number  = {12},
	pages   = {601--607}
}

@book{kuipers-niederreiter-1974,
	author    = {Kuipers, Lauwerens and Niederreiter, Harald},
	title     = {Uniform distribution of sequences},
	note      = {Pure and Applied Mathematics},
	publisher = {Wiley-Interscience},
	year      = {1974}
}

@incollection{laurent-2009,
	author    = {Laurent, Michel},
	title     = {On transfer inequalities in {D}iophantine approximation},
	booktitle = {Analytic number theory},
	pages     = {306--314},
	publisher = {Cambridge Univ. Press, Cambridge},
	year      = {2009}
}

@article{mazur-2008,
	author  = {Mazur, Barry},
	title   = {Finding meaning in error terms},
	journal = {Bull. Amer. Math. Soc. (N.S.)},
	volume  = {45},
	year    = {2008},
	number  = {2},
	pages   = {185--228}
}

@book{neukirch-schmidt-winberg-2008,
	author    = {Neukirch, J{\"u}rgen and Schmidt, Alexander and Wingberg, Kay},
	title     = {Cohomology of number fields},
	series    = {Grundlehren der Mathematischen Wissenschaften},
	volume    = {323},
	edition   = {Second},
	publisher = {Springer-Verlag},
	year      = {2008}
}

@article{niederreiter-1991,
	author  = {Niederreiter, Harald},
	title   = {The distribution of values of {K}loosterman sums},
	journal = {Arch. Math. (Basel)},
	volume  = {56},
	year    = {1991},
	number  = {3},
	pages   = {270--277} 
}

@article{okten-1999,
	author  = {\"Okten, Giray},
	title   = {Error reduction techniques in quasi-{M}onte {C}arlo integration},
	journal = {Math. Comput. Modelling},
	volume  = {30},
	date    = {1999},
	number  = {7-8},
	pages   = {61--69}
}

@article {pande-2011,
	author  = {Pande, Aftab},
	title   = {Deformations of {G}alois representations and the theorems of {S}ato--{T}ate and {L}ang--{T}rotter},
	journal = {Int. J. Number Theory},
	volume  = {7},
	year    = {2011},
	number  = {8},
	pages   = {2065--2079}
}

@article{ramakrishna-1999,
	author  = {Ramakrishna, Ravi},
	title   = {Lifting {G}alois representations},
	journal = {Invent. Math.},
	volume  = {138},
	year    = {1999},
	number  = {3},
	pages   = {537--562}
}

@article{ramakrishna-2002,
	author  = {Ramakrishna, Ravi},
	title   = {Deforming {G}alois representations and the conjectures of {S}erre and {F}ontaine--{M}azur},
	journal = {Ann. of Math. (2)},
	volume  = {156},
	year    = {2002},
	number  = {1},
	pages   = {115--154}
}

@misc{rosengarten-2013,
	author = {Rosengarten, Zev},
	title  = {An {E}rd{\"o}s--{T}ur{\'a}n Inequality For Compact Simply-Connected Semisimple Lie Groups},
	year   = {2013},
	note   = {arXiv:1305.2458},
}

@article{roth-1955,
	author  = {Roth, Klaus Friedrich},
	title   = {Rational approximations to algebraic numbers},
	journal = {Mathematika},
	volume  = {2},
	year    = {1955},
	pages   = {1--20}
}

@misc{rouse-thorner-2016,
	author = {Rouse, Jeremy and Thorner, Jesse},
	title  = {The explicit {S}ato--{T}ate conjecture and densities pertaining to {L}ehmer-type questions},
	year   = {2016},
	note   = {arXiv:1305.5283}
}

@misc{sarnak-2007,
	author = {Sarnak, Peter},
	title  = {Letter to: {B}arry {M}azur on ``{C}hebyshev's bias'' for $\tau(p)$},
	year   = {2007}
}

@article{serre-1981,
	author  = {Serre, Jean-Pierre},
	title   = {Quelques applications du th\'eor\`eme de densit\'e de {C}hebotarev},
	journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	number  = {54},
	year    = {1981},
	pages   = {323--401}
}

@book{serre-1989,
	author    = {Serre, Jean-Pierre},
	title     = {Abelian {$l$}-adic representations and elliptic curves},
	series    = {Advanced Book Classics},
	edition   = {Second},
	publisher = {Addison-Wesley},
	year      = {1989}
}

@incollection{serre-1994,
	author    = {Serre, Jean-Pierre},
	title     = {Propri\'et\'es conjecturales des groupes de {G}alois motiviques et des repr\'esentations {$l$}-adiques},
	booktitle = {Motives ({S}eattle, {WA}, 1991)},
	series    = {Proc. Sympos. Pure Math.},
	volume    = {55},
	pages     = {377--400},
	publisher = {Amer. Math. Soc., Providence, RI},
	year      = {1994}
}

@article{serre-tate-1968,
	author  = {Serre, Jean-Pierre and Tate, John},
	title   = {Good reduction of abelian varieties},
	journal = {Ann. of Math. (2)},
	volume  = {88},
	year    = {1968},
	pages   = {492--517}
}

@book{silverman-2009,
	author    = {Silverman, Joseph},
	title     = {The arithmetic of elliptic curves},
	series    = {Graduate Texts in Mathematics},
	volume    = {106},
	edition   = {Second},
	publisher = {Springer},
	year      = {2009}
}

@article{taylor-2003,
	author  = {Taylor, Richard},
	title   = {On icosahedral {A}rtin representations. {II}},
	journal = {Amer. J. Math.},
	volume  = {125},
	year    = {2003},
	number  = {3},
	pages   = {549--566}
}

@article{taylor-2008,
	author  = {Taylor, Richard},
	title   = {Automorphy for some {$l$}-adic lifts of automorphic mod {$l$} {G}alois representations. {II}},
	journal = {Publ. Math. Inst. Hautes \'Etudes Sci.},
	number  = {108},
	year    = {2008},
	pages   = {183--239}
}

@book{tenenbaum-1995,
	author    = {Tenenbaum, G\'erald},
	title     = {Introduction to analytic and probabilistic number theory},
	series    = {Cambridge Studies in Advanced Mathematics},
	volume    = {46},
	publisher = {Cambridge University Press},
	year      = {1995}
}

@article{yu-2015,
	author  = {Yu, Chia-Fu},
	title   = {A note on the {M}umford--{T}ate conjecture for {CM} abelian varieties},
	journal = {Taiwanese J. Math.},
	volume  = {19},
	year    = {2015},
	number  = {4},
	pages   = {1073--1084}
}