Residue classes of the partition function
Author:
D. W. MacLean
Journal:
Math. Comp. 34 (1980), 313317
MSC:
Primary 1004; Secondary 10A45
MathSciNet review:
551308
Fulltext PDF Free Access
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
(37 #2690)
 [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
(35 #5390), http://dx.doi.org/10.1090/S00029947196702145407
 [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. 133159.
 [5]
Torleiv
Kløve, Density problems for 𝑝(𝑛), J.
London Math. Soc. (2) 2 (1970), 504–508. MR 0265309
(42 #219)
 [6]
O.
Kolberg, Note on the parity of the partition function, Math.
Scand. 7 (1959), 377–378. MR 0117213
(22 #7995)
 [7]
D.
H. Lehmer, On the series for the partition
function, Trans. Amer. Math. Soc.
43 (1938), no. 2,
271–295. MR
1501943, http://dx.doi.org/10.1090/S00029947193815019435
 [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
(19,1160b)
 [9]
Morris
Newman, Periodicity modulo 𝑚 and
divisibility properties of the partition function, Trans. Amer. Math. Soc. 97 (1960), 225–236. MR 0115981
(22 #6778), http://dx.doi.org/10.1090/S00029947196001159812
 [10]
Morris
Newman, Note on partitions modulo 5,
Math. Comp. 21 (1967), 481–482. MR 0227127
(37 #2712), http://dx.doi.org/10.1090/S00255718196702271270
 [11]
Thomas
R. Parkin and Daniel
Shanks, On the distribution of parity in the
partition function, Math. Comp. 21 (1967), 466–480. MR 0227126
(37 #2711), http://dx.doi.org/10.1090/S00255718196702271269
 [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. 97128.
 [1]
 A. O. L. ATKIN, "Multiplicative congruence properties and density problems for ," Proc. London Math. Soc. (3), v. 18, 1968, pp. 563567. MR 0227105 (37:2690)
 [2]
 A. O. L. ATKIN & J. N. O'BRIEN, "Some properties of and modulo powers of 13," Trans. Amer. Math. Soc., v. 126, 1967, pp. 442459. MR 0214540 (35:5390)
 [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. 133159.
 [5]
 TORLEIV KLØVE, "Density problems for ," J. London Math. Soc. (2), v. 2, 1970, pp. 504508. MR 0265309 (42:219)
 [6]
 O. KOLBERG, "Note on the parity of the partition function," Math. Scand., v. 7, 1959, pp. 377378. MR 0117213 (22:7995)
 [7]
 D. H. LEHMER, "On the series for the partition function," Trans. Amer. Math. Soc., v. 43, 1938, pp. 271295. MR 1501943
 [8]
 MORRIS NEWMAN, "Congruences for the coefficients of modular forms and some new congruences for the partition function," Canad. J. Math., v. 9, 1957, pp. 549552. MR 0092801 (19:1160b)
 [9]
 MORRIS NEWMAN, "Periodicity modulo m and the divisibility properties of the partition function," Trans. Amer. Math. Soc., v. 97, 1960, pp. 225236. MR 0115981 (22:6778)
 [10]
 MORRIS NEWMAN, "Note on partitions modulo 5," Math. Comp., v. 21, 1967, pp. 481482. MR 0227127 (37:2712)
 [11]
 THOMAS R. PARKIN & DANIEL SHANKS, "On the distribution of parity in the partition function," Math. Comp., v. 21, 1967, pp. 466480. MR 0227126 (37:2711)
 [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. 97128.
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
1004,
10A45
Retrieve articles in all journals
with MSC:
1004,
10A45
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198005513086
PII:
S 00255718(1980)05513086
Article copyright:
© Copyright 1980
American Mathematical Society
