Efficient implementation of the Hardy–Ramanujan–Rademacher formula

DOI10.1112/S1461157012001088zbMath1344.11089arXiv1205.5991WikidataQ59444666 ScholiaQ59444666MaRDI QIDQ5169644

Fredrik Johansson

Publication date: 11 July 2014

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.5991

zbMATH Keywords

partition functionmulti-evaluation of partition function

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81) Software, source code, etc. for problems pertaining to number theory (11-04) Calculation of integer sequences (11Y55)

Related Items

Fast computation of the partition function, Will the real Hardy-Ramanujan formula please stand up?, Formulas for the number of partitions related to the Rogers-Ramanujan identities, Infinite families of crank functions, Stanton-type conjectures, and unimodality, Probabilistic divide-and-conquer: deterministic second half, Relations among Ramanujan-type congruences II: Ramanujan-type congruences in half-integral weights, Scarcity of congruences for the partition function, Efficient computation of the overpartition function and applications, Class polynomials for nonholomorphic modular functions, Probabilistic Divide-and-Conquer: A New Exact Simulation Method, With Integer Partitions as an Example, Congruences satisfied by eta-quotients, Complementary Schur asymptotics for partitions, On the number of partitions into parts not congruent to \(0, \pm 3\pmod{12}\), On a nonlinear relation for computing the overpartition function, Congruences like Atkin’s for the partition function

Uses Software

• FLINT
• gmp
• PARI/GP
• SageMath
• MPFR
• MPIR
• OEIS
• FDLIBM

Cites Work

• The average least quadratic nonresidue modulo \(m\) and other variations on a theme of Erdős
• A sum connected with the series for the partition function
• Distribution of the partition function modulo \(m\)
• The least quadratic non residue
• A ONE LINE FACTORING ALGORITHM
• The Minimal Polynomial of cos(2π/n)
• Computing the integer partition function
• Accuracy and Stability of Numerical Algorithms
• On a Conjecture of Ramanujan
• On the Partition Function p (n )
• On the Hardy-Ramanujan Series for the Partition Function
• Theorems on Dedekind Sums
• New congruences for the partition function
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