Residue classes of the partition function

Author:
D. W. MacLean

Journal:
Math. Comp. **34** (1980), 313-317

MSC:
Primary 10-04; Secondary 10A45

DOI:
https://doi.org/10.1090/S0025-5718-1980-0551308-6

MathSciNet review:
551308

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The results of computations of for primes are summarized in frequency tables of residue classes.

**[1]**A. O. L. Atkin,*Multiplicative congruence properties and density problems for 𝑝(𝑛)*, Proc. London Math. Soc. (3)**18**(1968), 563–576. MR**0227105**, https://doi.org/10.1112/plms/s3-18.3.563**[2]**A. O. L. Atkin and J. N. O’Brien,*Some properties of 𝑝(𝑛) and 𝑐(𝑛) modulo powers of 13*, Trans. Amer. Math. Soc.**126**(1967), 442–459. MR**0214540**, https://doi.org/10.1090/S0002-9947-1967-0214540-7**[3]**H. GUPTA, A. E. GWYTHER & J. C. P. MILLER, "Tables of partitions,"*Roy. Soc. Math. Tables*, v. 4, 1958.**[4]**TORLEIV KLØVE, "Recurrence formulae for the coefficients of modular forms and congruences for the partition function and for the coefficients of , and ,"*Math. Scand.*, v. 23, 1968, pp. 133-159.**[5]**Torleiv Kløve,*Density problems for 𝑝(𝑛)*, J. London Math. Soc. (2)**2**(1970), 504–508. MR**0265309**, https://doi.org/10.1112/jlms/2.Part_3.504**[6]**O. Kolberg,*Note on the parity of the partition function*, Math. Scand.**7**(1959), 377–378. MR**0117213**, https://doi.org/10.7146/math.scand.a-10584**[7]**D. H. Lehmer,*On the series for the partition function*, Trans. Amer. Math. Soc.**43**(1938), no. 2, 271–295. MR**1501943**, https://doi.org/10.1090/S0002-9947-1938-1501943-5**[8]**Morris Newman,*Congruences for the coefficients of modular forms and some new congruences for the partition function*, Canad. J. Math.**9**(1957), 549–552. MR**0092801**, https://doi.org/10.4153/CJM-1957-062-1**[9]**Morris Newman,*Periodicity modulo 𝑚 and divisibility properties of the partition function*, Trans. Amer. Math. Soc.**97**(1960), 225–236. MR**0115981**, https://doi.org/10.1090/S0002-9947-1960-0115981-2**[10]**Morris Newman,*Note on partitions modulo 5*, Math. Comp.**21**(1967), 481–482. MR**0227127**, https://doi.org/10.1090/S0025-5718-1967-0227127-0**[11]**Thomas R. Parkin and Daniel Shanks,*On the distribution of parity in the partition function*, Math. Comp.**21**(1967), 466–480. MR**0227126**, https://doi.org/10.1090/S0025-5718-1967-0227126-9**[12]**S. RAMANUJAN, "Congruence properties of partitions,"*Proc. London Math. Soc.*(2), v. 18, 1920.**[13]**G. N. WATSON, "Ramanujan's Vermutung über Zerfällungsanzahlen,"*J. Reine Angew. Math.*, v. 179, 1938, pp. 97-128.

Retrieve articles in *Mathematics of Computation*
with MSC:
10-04,
10A45

Retrieve articles in all journals with MSC: 10-04, 10A45

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0551308-6

Article copyright:
© Copyright 1980
American Mathematical Society