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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…
Comprehensive textbook provides both mathematicians and applied scientists with a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation. Luci…
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…
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…
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.
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…
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…
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…
