… The method employed in the present paper depends in part on showing that A k(n) may be
transformed into "generalized Kloosterman sums." These in turn may be evaluated by a slight …

… equals the number of partitions of n into distinct, odd parts. We also establish various
generalizations of Lehmer's identity, and prove related Beck-type companion identities. We use …

… However for d>0 such sets of parts depend on s and so such partitions … on the one hand
(in view of (14)) and 3d+3 on the other, since d<z3. We now consider the coefficient of xdd+* on …

… If the parts a, are restricted to a, set S of positive integers and if we add the weights of all
the partitions of n into parts taken from S we obtain … a rational number we call informally …

… comma England on a Guggenheim Fellowship comma during which time the Lehmers met
Hardy … The work of DHL on the partition function p open parenthesis n closing parenthesis is …

… 3), except for an affirmative test by DH Lehmer 6 of an isolated value. … In order to have
a check on the coefficients of Ell, we observe that, by an elementary theorem on binomial …

… under DH Lehmer at Berkeley and remained one year as an instructor. Since (except for a
Zurich … on the right hand side of (6) into the sum on the left hand side by use of Jacobi's identity …

… partition of n by + I or - I according as the number of parts is even or odd. There being only
one partition … We dismiss this real valued function as trivial and from now on consider k;;;. 3. …

… If m is an odd prime p, we have already seen (in section 1) the effect of degeneracy on the …
two generalizations of the preceding theorem depending on the parity of m. THEOREM 2.3. If …

… method for evaluating and factorizing Ak (n) based on a different expression for … Then we
have the identity … It should be pointed out that our theorems and Lehmer's theorems overlap to a …