The Cartan-Kähler theorem demonstrates that certain real analytic exterior differential systems--ones which Cartan dubbed "involutive"--admit local real analytic solutions. The proof reduces the system to a set of determined systems of PDE's which are then solved using the Cauch…
Paper I is concerned with computational aspects of the Selberg trace formalism, considering the usual type of eigenfunction and including an analysis of pseudo cusp forms and their residual effects. Paper II examines the modular group PSL (2, [bold]Z), as such groups have both a…
This paper is concerned with the spectral theory of the Laplacian as the underlying Riemann surface is "pinched down" to a surface with nodes. The problem is attacked from the (general) standpoint of regular b-groups and the Selberg trace formula.
The first part of Chapter 16 in Ramanujan's second notebook is devoted to q-series. Several of the results obtained by Ramanujan are classical, but many are new. In particular, certain elegant q-continued fraction expansions have not appeared heretofore in print. In the remainde…
Path functions and their basic properties are obtained by extending the constructive theory of partition generating functions developed by Sylvester, Durfee, Andrews and others. Path functions also arise when we have an expansion of a function satisfying a linear difference equa…
Blaschke rolling theorem in its original form dealt with the problem of finding sufficient conditions for a ball [italic]D₁ to roll freely inside a compact convex set [italic]D₂ with a non-empty interior. The paper is divided into two parts. Part I is primarily concerned with pr…
In this memoir, Yang-Mills field curvature and current are described as elements of cohomology groups on ambitwistor space, and it is shown that the Yang-Mills current corresponds to the third-order obstruction to extending the corresponding vector bundle. There is also a descri…
Maximal functions which measure the smoothness of a function are introduced and studied from the point of view of their relationship to classical smoothness and their use in proving embedding theorems, extension theorems, and various results on differentiation. New spaces of fun…
Werke des deutschen Mathematikers Ernst Eduard Kummer, dessen Einführung von Idealzahlen, die als spezielle Untergruppe eines Rings definiert sind, den Grundsatz der Arithmetik (eindeutige Faktorisierung jeder ganzen Zahl zu einem Produkt von Primzahlen) auf komplexe Zahlenfelde…
This is the fourth edition of Serge Lang's Complex Analysis. The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series meth…
"This is the fourth edition of Serge Lang's Complex Analysis. The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series met…
"Commencing with Gauss, mathematicians have contributed to the study in the plane of the complex variable of the geometric relations between the zeros of a polynomial and those of its derivative. More generally there have been studied the relations between the zeros and poles of…
