modular%20form
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5 matching pages
1: Software Index
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Open Source Collections and Systems.
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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20 Theta Functions | |||||||||||||||||||||||||
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23 Weierstrass Elliptic and Modular Functions | |||||||||||||||||||||||||
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These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.
2: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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Modular Forms and Fermat’s Last Theorem.
Springer-Verlag, New York.
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Algorithms for Modular Elliptic Curves.
2nd edition, Cambridge University Press, Cambridge.
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3: 27.2 Functions
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►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
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►An equivalent form states that the th prime (when the primes are listed in increasing order) is asymptotic to as :
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27.2.8
►and if is the smallest positive integer such that , then is a primitive root mod .
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4: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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A vortex filament moving without change of form.
J. Fluid Mech. 112, pp. 397–409.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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Introduction to Elliptic Curves and Modular Forms.
2nd edition, Graduate Texts in Mathematics, Vol. 97, Springer-Verlag, New York.
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5: Bibliography M
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Siegel’s modular forms and Dirichlet series.
Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin.
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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An integral representation for the Bessel form.
J. Comput. Appl. Math. 57 (1-2), pp. 251–260.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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