\begin{thebibliography}{10}

\bibitem{BaHo62}
P.~T. Bateman and R.~A. Horn, A heuristic asymptotic formula concerning the
  distribution of prime numbers, {\em Math. Comp.} {\bf 16} (1962), 363--367.

\bibitem{parigp}
K.~{Belabas et al.}, {\em PARI/GP}.
\newblock Bordeaux, 2.7.5 edition, November 2015.
\newblock \url{http://pari.math.u-bordeaux.fr/}.

\bibitem{Bernstein2008}
D.~J. Bernstein, Fast multiplication and its applications.
\newblock In {\em Algorithmic Number Theory}, Vol.~44, pp.  325--384. MSRI
  Publications, 2008.

\bibitem{ChCh88}
{D. V.} Chudnovsky and {G. V.} Chudnovsky, Approximations and complex
  multiplication according to {R}amanujan, In {\em Ramanujan Revisited}, pp.
  375--472. Academic Press, 1988.
\newblock Proceedings of the Centenary Conference, University of Illinois at
  Urbana-Champaign, June 1--5, 1987.

\bibitem{Cohen00}
H.~Cohen, {\em Advanced Topics in Computational Number Theory}, Vol. 193 of
  {\em Graduate Texts in Mathematics}, Springer-Verlag, 2000.

\bibitem{CoFrAvDoLaNgVe06}
H.~Cohen, G.~Frey, R.~Avanzi, C.~Doche, T.~Lange, K.~Nguyen, and
  F.~Vercauteren, {\em Handbook of Elliptic and Hyperelliptic Curve
  Cryptography}, Discrete mathematics and its applications, Chapman \&
  Hall/CRC, 2006.

\bibitem{Cox89}
D.~A. Cox, {\em Primes of the Form $x^2 + n y^2$ --- {F}ermat, Class Field
  Theory, and Complex Multiplication}, John Wiley \& Sons, 1989.

\bibitem{Dickson23}
L.~E. Dickson, {\em History of the Theory of Numbers}, Vol. III --- Quadratic
  and Higher Forms, Carnegie Institution of Washington, 1923.

\bibitem{DoLi80}
D.~Dobkin and R.~J. Lipton, Addition chain methods for the evaluation of
  specific polynomials, {\em SIAM J. Comput.} {\bf 9} (1980), 121--125.

\bibitem{DoLeSe81}
P.~Downey, B.~Leong, and R.~Sethi, Computing sequences with addition chains,
  {\em SIAM J. Comput.} {\bf 10} (1981), 638--646.

\bibitem{Dupont11}
R.~Dupont, Fast evaluation of modular functions using {N}ewton iterations and
  the {AGM}, {\em Math. Comp.} {\bf 80} (2011), 1823--1847.

\bibitem{Enge09cla}
A.~Enge, The complexity of class polynomial computation via floating point
  approximations, {\em Math. Comp.} {\bf 78} (2009), 1089--1107.

\bibitem{Enge09mod}
A.~Enge, Computing modular polynomials in quasi-linear time, {\em Math. Comp.}
  {\bf 78} (2009), 1809--1824.

\bibitem{cm}
A.~Enge, {\em CM --- Complex multiplication of elliptic curves}.
\newblock INRIA, 0.2.1 edition, March 2015.
\newblock Distributed under GPL v2+, \url{http://cm.multiprecision.org/}.

\bibitem{EnMo14}
A.~Enge and F.~Morain, Generalised {W}eber functions, {\em Acta Arith.} {\bf
  164} (2014), 309--341.

\bibitem{EnSc04}
A.~Enge and R.~Schertz, Constructing elliptic curves over finite fields using
  double eta-quotients, {\em J. Th\'eor. Nombres Bordeaux} {\bf 16} (2004),
  555--568.

\bibitem{EnSc13}
A.~Enge and R.~Schertz, Singular values of multiple eta-quotients for ramified
  primes, {\em LMS J. Comput. Math.} {\bf 16} (2013), 407--418.

\bibitem{Euler55}
L.~Euler, Letter to {G}oldbach, 23 August 1755.
\newblock \url {http://eulerarchive.maa.org/correspondence/letters/OO0887.pdf}.

\bibitem{Euler58}
L.~Euler, De numeris, qui sunt aggregata duorum quadratorum, {\em Novi
  commentarii academiae scientiarum Petropolitanae} {\bf 4} (1758), 3--40.
\newblock English translation at \url
  {http://eulerarchive.maa.org/pages/E228.html}.

\bibitem{Euler60}
L.~Euler, Demonstratio theorematis fermatiani omnem numerum primum formae
  $4n+1$ esse summam duorum quadratorum, {\em Novi commentarii academiae
  scientiarum Petropolitanae} {\bf 5} (1760), 3--58.
\newblock English translation at \url
  {http://eulerarchive.maa.org/pages/E241.html}.

\bibitem{Euler61}
L.~Euler, Specimen de usu observationum in mathesi pura, {\em Novi commentarii
  academiae scientiarum Petropolitanae} {\bf 6} (1761), 185--230.
\newblock \url {http://eulerarchive.maa.org/pages/E241.html}.

\bibitem{Euler83}
L.~Euler, Evolutio producti infiniti $(1 - x)(1 - xx)(1 - x^3) (1 - x^4)(1 -
  x^5)(1 - x^6)$ etc. in seriem simplicem, {\em Acta Academiae Scientiarum
  Imperialis Petropolitanae} {\bf 1780} (1783), 47--55.

\bibitem{Gauss01}
C.~F. Gau{\ss}, {\em Disquisitiones Arithmeticae}, Gerh. Fleischer Jun., 1801.

\bibitem{Grosswald85}
E.~Grosswald, {\em Representations of Integers as Sums of Squares},
  Springer-Verlag, 1985.

\bibitem{mpir}
W.~Hart, {\em MPIR -- Multiple Precision Integers and Rationals}, 2.7.2
  edition, 2015.
\newblock \url{http://mpir.org/}.

\bibitem{Hirschhorn09}
M.~D. Hirschhorn, The number of representations of a number by various forms
  involving triangles, squares, pentagons and octagons, In Nayandeep~Deka
  Baruah, Bruce~C. Berndt, Shaun Cooper, Tim Huber, and Michael Schlosser,
  editors, {\em Ramanujan Rediscovered}, Vol.~14 of {\em RMS Lecture Notes
  Series}, pp.  113--124, Mysore, 2009. Ramanujan Mathematical Society.

\bibitem{Johansson14}
F.~Johansson, Evaluating parametric holonomic sequences using rectangular
  splitting, In {\em Proceedings of the 39th International Symposium on
  Symbolic and Algebraic Computation}, ISSAC `14, pp.  256--263, New York, NY,
  USA, 2014. ACM.

\bibitem{Arb}
F.~Johansson, {\em Arb -- C library for arbitrary-precision ball arithmetic}.
\newblock INRIA, 2.8.1 edition, 2015.
\newblock \url{http://arblib.org/}.

\bibitem{Knuth98}
D.~E. Knuth, {\em The Art of Computer Programming, volume 2: Seminumerical
  Algorithms}, Addison-Wesley, 3rd edition, 1998.

\bibitem{Legendre97}
A.~M. {le Gendre}, {\em Essai sur la Th\'eorie des Nombres}, Duprat, 1797.
\newblock \url {http://gallica.bnf.fr/ark:/12148/btv1b8626880r}.

\bibitem{Mumford83}
D.~Mumford, {\em Tata Lectures on Theta I}, Birkh\"auser, 1983.

\bibitem{Mumford84}
D.~Mumford, {\em Tata Lectures on Theta II --- Jacobian Theta Functions and
  Differential Equations}, Birkh\"auser, 1984.

\bibitem{Mumford91}
D.~Mumford, {\em Tata Lectures on Theta III}, Birkh\"auser, 1991.

\bibitem{PaSt73}
M.~S. Paterson and L.~J. Stockmeyer, On the number of nonscalar multiplications
  necessary to evaluate polynomials, {\em SIAM J. Comput.} {\bf 2} (1973),
  60--66.

\bibitem{Rademacher38}
H.~Rademacher, The {F}ourier coefficients of the modular invariant $j(\tau)$,
  {\em Amer. J. Math.} {\bf 60} (1938), 501--512.

\bibitem{RoSc62}
J.~B. Rosser and L.~Schoenfeld, Approximate formulas for some functions of
  prime numbers, {\em Illinois J. Math.} {\bf 6} (1962), 64--94.

\bibitem{Schertz02}
R.~Schertz, Weber's class invariants revisited, {\em J. Th\'eor. Nombres
  Bordeaux} {\bf 14} (2002), 325--343.

\bibitem{Smith1989}
D.~M. Smith, Efficient multiple-precision evaluation of elementary functions,
  {\em Math. Comp.} {\bf 52} (1989), 131--134.

\bibitem{Weber08}
H.~Weber, {\em Lehrbuch der {A}lgebra}, Vol. 3: \textit {Elliptische Funktionen
  und alge\-brai\-sche Zahlen}, Vieweg, 2nd edition, 1908.

\end{thebibliography}