Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 21, Number 4

#### Publication Date: December 1954

A note on the series $\sum a_nf(nz)$

J. M. Whittaker; 571-573

Generalized local class field theory III. Second form of existence theorem. Structure of analytic groups.

G. Whaples; 575-581

Generalized local class field theory IV. Cardinalities

G. Whaples; 583-586

Riemann’s localization theorem for Fourier series

Einar Hille and George Klein; 587-591

Sets of convergence of ordinary Dirichlet series

George Brauer; 593-594

Uniform completeness of sets of reciprocals of linear functions. II

Pasquale Porcelli; 595-597

Representatives of homotopy classes of mappings into spheres

Robert L. Plunkett; 599-605

Prime divisors of second order recurring sequences

Morgan Ward; 607-614

The enclosing of simple arcs and curves by polyhedra

O. G. Harrold, Jr.; 615-621

The translation pathology of Wiener space

R. H. Cameron; 623-627

The distribution of squarefree integers in small intervals

Richard Bellman and Harold N. Shapiro; 629-637

Approximations to monotone mappings on non-compact two dimensional manifolds

John G. Hocking; 639-651

Complex biorthogonality for certain sets of polynomials

Philip Davis and Henry Pollak; 653-667

Congruences for the solutions of certain difference equations of the second order

L. Carlitz; 669-679

Maximal ideals in compact semigroups

R. J. Koch and A. D. Wallace; 681-685