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A problem on partitions with a prime modulus 
Author:
Peter Hagis
Journal:
Trans. Amer. Math. Soc. 102 (1962), 30-62
MSC:
Primary 10.48
MathSciNet review:
0146166
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- [1]
Emil
Grosswald, Some theorems concerning
partitions, Trans. Amer. Math. Soc. 89 (1958), 113–128. MR 0097371
(20 #3840), http://dx.doi.org/10.1090/S0002-9947-1958-0097371-5
- [2]
G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatorial analysis, Proc. London Math. Soc. (2) 17 (1918), 75-115.
- [3]
Joseph
Lehner, A partition function connected with the modulus five,
Duke Math. J. 8 (1941), 631–655. MR 0005523
(3,166b)
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John
Livingood, A partition function with the prime modulus
𝑃>3, Amer. J. Math. 67 (1945),
194–208. MR 0012101
(6,259b)
- [5]
Hans
Petersson, Über Modulfunktionen und Partitionenprobleme,
Abh. Deutsch. Akad. Wiss. Berlin. Kl. Math. Allg. Nat.
1954 (1954), no. 2, 59 (German). MR 0071458
(17,129b)
- [6]
Hans
Petersson, Über die arithmetischen Eigenschaften eines Systems
multiplikativer Modulfunktionen von Primzahlstufe, Acta Math.
95 (1956), 57–110 (German). MR 0077566
(17,1057f)
- [7]
H. Rademacher, On the partition function
, Proc. London Math. Soc. (2) 43 (1937), 241-254.
- [8]
Hans
Rademacher, The Fourier Coefficients of the Modular Invariant
J(𝜏), Amer. J. Math. 60 (1938), no. 2,
501–512. MR
1507331, http://dx.doi.org/10.2307/2371313
- [9]
Hans
Rademacher and Herbert
S. Zuckerman, On the Fourier coefficients of certain modular forms
of positive dimension, Ann. of Math. (2) 39 (1938),
no. 2, 433–462. MR
1503417, http://dx.doi.org/10.2307/1968796
- [10]
Hans
Rademacher and Albert
Whiteman, Theorems on Dedekind sums, Amer. J. Math.
63 (1941), 377–407. MR 0003650
(2,249f)
- [11]
Hans
Salié, Zur Abschätzung der Fourierkoeffizienten ganzer
Modulformen, Math. Z. 36 (1933), no. 1,
263–278 (German). MR
1545344, http://dx.doi.org/10.1007/BF01188622
- [12]
H. J. Smith, Collected math. papers, Vol. 2, Clarendon Press, Oxford, 1894.
- [13]
Heinrich
Tietze, Ein zweiter Beweis eines Satzes über Partitionen,
S.-B. Math.-Nat. Abt. Bayer. Akad. Wiss. 1947 (1947),
45–46 (German). MR 0024935
(9,571a)
- [14]
G. N. Watson, A treatise on the theory of Bessel functions, Cambridge, 1922.
- [1]
- E. Grosswald, Some theorems concerning partitions, Trans. Amer. Math. Soc. 89 (1958), 113-128. MR 0097371 (20:3840)
- [2]
- G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatorial analysis, Proc. London Math. Soc. (2) 17 (1918), 75-115.
- [3]
- J. Lehner, A partition function connected with the modulus five, Duke Math. J. 8 (1941), 631-655. MR 0005523 (3:166b)
- [4]
- J. Livingood, A partition function with the prime modulus
, Amer. J. Math. 67 (1945), 194-208. MR 0012101 (6:259b)
- [5]
- H. Petersson, Über Modulfunktionen und Partitionenprobleme, Abh. Deutsch. Akad. Wiss. Berlin Kl. Math. Allg. Nat. 1954, No. 2. MR 0071458 (17:129b)
- [6]
- -, Über die arithmetischen Eigenschaften eines Systems multiplikativer Modulfunktionen von Primzahlstufe, Acta Math. 95 (1956), 57-110. MR 0077566 (17:1057f)
- [7]
- H. Rademacher, On the partition function
, Proc. London Math. Soc. (2) 43 (1937), 241-254.
- [8]
- -, The Fourier coefficients of the modular invariant
, Amer J. Math. 60 (1938), 501-512. MR 1507331
- [9]
- H. Rademacher and H. Zuckerman, On the Fourier coefficients of certain modular forms of positive dimension, Ann. of Math. 39 (1938), 433-462. MR 1503417
- [10]
- H. Rademacher and A. Whiteman, Theorems on Dedekind sums, Amer. J. Math. 63 (1941), 377-407. MR 0003650 (2:249f)
- [11]
- H. Salié, Zur Abschatzung der Fourierkoeffizienten ganzer Modulformen, Math. Z. 36 (1933), 263-278. MR 1545344
- [12]
- H. J. Smith, Collected math. papers, Vol. 2, Clarendon Press, Oxford, 1894.
- [13]
- H. Tietze, Ein zweiter Beweis eines Satzes über Partitionen, S.-B. Math.-Nat. Abt. Bayer. Akad. Wiss. 1947, 45-46 (1947). MR 0024935 (9:571a)
- [14]
- G. N. Watson, A treatise on the theory of Bessel functions, Cambridge, 1922.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1962-0146166-3
PII:
S 0002-9947(1962)0146166-3
Article copyright:
© Copyright 1962 American Mathematical Society
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