Density problems involving $p_{r}(n)$

Author:
Patrick J. Costello

Journal:
Math. Comp. **38** (1982), 633-637

MSC:
Primary 10A45

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645678-X

MathSciNet review:
645678

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Abstract | References | Similar Articles | Additional Information

Abstract: Lower bounds on the density of zeros of ${p_r}(n)$ are provided for certain values of *r*.

- Tom M. Apostol,
*Introduction to analytic number theory*, Springer-Verlag, New York-Heidelberg, 1976. Undergraduate Texts in Mathematics. MR**0434929** - A. O. L. Atkin,
*Proof of a conjecture of Ramanujan*, Glasgow Math. J.**8**(1967), 14–32. MR**205958**, DOI https://doi.org/10.1017/S0017089500000045 - A. O. L. Atkin,
*Multiplicative congruence properties and density problems for $p(n)$*, Proc. London Math. Soc. (3)**18**(1968), 563–576. MR**227105**, DOI https://doi.org/10.1112/plms/s3-18.3.563 - R. P. Bambah,
*Two congruence properties of Ramanujan’s function $\tau (n)$*, J. London Mth. Soc.**21**(1946), 91–93. MR**0019665** - R. P. Bambah,
*Ramanujan’s function $\tau (n)$—a congruence property*, Bull. Amer. Math. Soc.**53**(1947), 764–765. MR**21553**, DOI https://doi.org/10.1090/S0002-9904-1947-08869-8 - Torleiv Kløve,
*Density problems for $p(n)$*, J. London Math. Soc. (2)**2**(1970), 504–508. MR**265309**, DOI https://doi.org/10.1112/jlms/2.Part_3.504 - D. H. Lehmer,
*Some functions of Ramanujan*, Math. Student**27**(1959), 105–116. MR**131412** - D. W. MacLean,
*Residue classes of the partition function*, Math. Comp.**34**(1980), no. 149, 313–317. MR**551308**, DOI https://doi.org/10.1090/S0025-5718-1980-0551308-6 - Morris Newman,
*An identity for the coefficients of certain modular forms*, J. London Math. Soc.**30**(1955), 488–493. MR**70658**, DOI https://doi.org/10.1112/jlms/s1-30.4.488 - Morris Newman,
*Some theorems about $p_r(n)$*, Canadian J. Math.**9**(1957), 68–70. MR**83520**, DOI https://doi.org/10.4153/CJM-1957-009-6 - Morris Newman,
*A table of the coefficients of the powers of $\eta (\tau )$*, Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math.**18**(1956), 204–216. MR**0076802**
S. Ramanujan,

*Collected Papers*, Chelsea, New York, 1927, pp. 210-213, 232-238. G. N. Watson, "Ramanujan’s Vermutung über Zerfallungsanzahlen,"

*J. Reine Angew. Math.*, v. 179, 1938, pp. 97-128.

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Article copyright:
© Copyright 1982
American Mathematical Society