Irving Gerst

Some infinite product identities

In this paper we derive the power series expansions of four infinite products of the form 1I (1Xn) 7 (1 + Xn), nES1 nES2 where the index sets Si and S2 are specified with respect to a modulus (Theorems 1, 3, and 4). We also establish a useful formula for expanding the product of two Jacobi triple products (Theorem 2). Finally, we give nonexistence results for identities of two forms.

Kinetics of protein synthesis by polyribosomes

Abstract A detailed deterministic model for the kinetics of protein synthesis is developed on the assumption that the kinetics of the system depends linearly on the messenger RNA concentration. While the concentration of such components as adaptor RNA and ribosomes are regarded as constant, the messenger RNA input is taken to be time dependent and the analysis is given for both step and ramp inputs. It is shown that the theory predicts a nonlinear build-up in protein concentration followed by a linear phase in agreement with some experimental results. The slope of the linear portion corresponds to the rate of messenger RNA production.

A computer-assisted investigation of Ramanujan pairs

Etude par ordinateur des paires {ai} et {bj} de Ramanujan liees par la relation πi≥1(1−x au i) −1 =1+∈j≥1 x bj /(1−x)(1−x 2 )...(1−x j ). Etablissement de nouvelles identites

On the mod 2 reciprocation of infinite modular-part products and the parity of certain partition functions

An infinite modular-part (MP) product is defined to be a product of the form Π n∈S (1−x n ), where S={n∈Z + / n≡r 1 ,...,r t (mod m)}. A complete method is developed which determines if a given MP product has an MP reciprocal modulo 2 and finds it if it does. Next, a graph-theoretic interpretation of this method is made from which a streamlined algorithm is derived for deciding whether the given MP product is such a reciprocal. This algorithm is applied to the single- variable Jacobi triple product and the quintuple product