This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic number fields, and with Eisenstein series. The author brings to the public the large number of identities that have been discovered over the past 20 years, the majority of which have not been published elsewhere. The book will be of interest to graduate students and scholars in the field of number theory and, in particular, modular forms. It is not an introductory text in this field. Nevertheless, some theoretical background material is presented that is important for understanding the examples in Part II of the book. In Part I relevant definitions and essential theorems -- such as a complete proof of the structure theorems for coprime residue class groups in quadratic number fields that are not easily accessible in the literature -- are provided. Another example is a thorough description of an algorithm for listing all eta products of given weight and level, together with proofs of some results on the bijection between these eta products and lattice simplices.

The subject matter of volume 2 of the 2-volumes-handbook focusses especially on rare sarcomas of the whole female genitalia. These entities include angiosarcoma, the different lipo- and rhabdomyosarcoma as well as newer entities like the PEComa. Furthermore, mixed mullerian tumors like the benign adenofibroma and the malignant adenosarcoma and carcinosarcoma are described in detail. The book provides a description at length of the epidemiology, etiology, pathological anatomy, prognosis, diagnosis, differential diagnosis, imaging and comprehensive therapy of each primary, relapsed, and metastasized tumor including surgery, chemo-, hormone- and radio- and targeted therapy. An own chapter is devoted to the problems of fertility and pregnancy in connection with all sarcomas, variants of leiomyoma, atypical smooth muscle tumors, disseminated peritoneal leiomyomatosis, benign metastasizing leiomyoma, intravenous leiomyomatosis and endometrial stromal tumors - endometrial stromal nodules, endometrial stromal tumor with sex cord-like elements (ESTSCLE), uterine tumor resembling ovarian sex-cord tumor (UTROSCT) -and all mixed tumors - of the female genitalia. The book aims to identify and provide diagnostic and therapeutic guidance. The listed tumor entities also constitute a particular diagnostic challenge for pathologists that contains numerous pitfalls and difficulties. This book, therefore, addresses gynecologists and pathologists in both clinical and private practice, but also surgeons and hemato-oncologists.

This book grew out of our lectures given in the Oberseminar on 'Cod ing Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001. The coding the ory combines mathematical elegance and some engineering problems to an unusual degree. The major advantage of studying coding theory is the beauty of this particular combination of mathematics and engineering. In this book we wish to introduce some practical problems to the math ematician and to address these as an essential part of the development of modern number theory. The book consists of five chapters and an appendix. Chapter 1 may mostly be dropped from an introductory course of linear codes. In Chap ter 2 we discuss some relations between the number of solutions of a diagonal equation over finite fields and the weight distribution of cyclic codes. Chapter 3 begins by reviewing some basic facts from elliptic curves over finite fields and modular forms, and shows that the weight distribution of the Melas codes is represented by means of the trace of the Hecke operators acting on the space of cusp forms. Chapter 4 is a systematic study of the algebraic-geometric codes. For a long time, the study of algebraic curves over finite fields was the province of pure mathematicians. In the period 1977 - 1982, V. D. Goppa discovered an amazing connection between the theory of algebraic curves over fi nite fields and the theory of q-ary codes."

This book grew out of our lectures given in the Oberseminar on 'Cod ing Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001. The coding the ory combines mathematical elegance and some engineering problems to an unusual degree. The major advantage of studying coding theory is the beauty of this particular combination of mathematics and engineering. In this book we wish to introduce some practical problems to the math ematician and to address these as an essential part of the development of modern number theory. The book consists of five chapters and an appendix. Chapter 1 may mostly be dropped from an introductory course of linear codes. In Chap ter 2 we discuss some relations between the number of solutions of a diagonal equation over finite fields and the weight distribution of cyclic codes. Chapter 3 begins by reviewing some basic facts from elliptic curves over finite fields and modular forms, and shows that the weight distribution of the Melas codes is represented by means of the trace of the Hecke operators acting on the space of cusp forms. Chapter 4 is a systematic study of the algebraic-geometric codes. For a long time, the study of algebraic curves over finite fields was the province of pure mathematicians. In the period 1977 - 1982, V. D. Goppa discovered an amazing connection between the theory of algebraic curves over fi nite fields and the theory of q-ary codes."

Die seltenen uterinen Sarkome und malignen Mischtumoren sind haufig ein Zufallsbefund. Neben nur wenigen aussagekraftigen Studien existieren keine definierten Therapiestandards und Leitlinien. Wegen der schwierigen Abgrenzung zu den Sarkomen und malignen Mischtumoren wurden auch die mesenchymalen Tumoren mit auffalligen klinischen Eigenschaften, einem potentiell klinisch malignen Verhalten und einem unsicherem malignen Potential aber auch gutartige Mischtumoren in die Publikation aufgenommen. Fur jede Entitat erfolgt eine detaillierte Besprechung zur Epidemiologie, AEtiologie und Pathogenese. Besonderer Wert wird auf die makro- und mikroskopische Charakterisierung, die Prognose sowie die Diagnostik und Differenzialdiagnose mit ihren Fallstricken und Fehlerquellen gelegt. Die klar formulierten Therapieempfehlungen behandeln jeweils auf den Uterus begrenzte, fortgeschrittene, rezidivierte und metastasierte Tumoren. Die Moeglichkeiten der Operation, der Bestrahlung, der neoadjuvanten, adjuvanten sowie palliativen Hormon- und Chemotherapie und Empfehlungen zur Nachsorge werden umfassend und kritisch dargestellt. Trotz der vergleichsweise ausfuhrlichen pathologisch-anatomischen Beschreibung, soll dieses Buch mit uber 200 hochwertigen, vierfarbigen Abbildungen und einem umfassenden aktuellen Literaturverzeichnis dennoch ein Leitfaden zur Entscheidungsfindung fur den klinisch und ambulant tatigen Gynakologen und Onkologen zu sein. Fur die aufgefuhrten Tumorgruppen existiert gegenwartig keine weitere zusammenfassende Monographie.

The subject matter of volume 1 of the 2-volumes-handbook focusses on leiomyosarcoma, low-grade and high-grade endometrial sarcoma and undifferentiated uterine sarcoma of the whole female genitalia. A separate extensive chapter is devoted to the variants of leiomyoma (angio-, lipo-, cotyledonoid, cellular, mitotically active, epithelioid and myxoid leiomyoma, leiomyoma with bizarre nuclei), atypical smooth muscle tumors (smooth muscle tumors with uncertain malignant potential), and disseminated peritoneal leiomyomatosis, benign metastasizing leiomyoma, and intravenous leiomyomatosis. Furthermore, endometrial stromal tumors - endometrial stromal nodules, endometrial stromal tumor with sex cord-like elements (ESTSCLE), uterine tumor resembling ovarian sex-cord tumor (UTROSCT) - and similar tumors are described in detail. The book provides a description at length of the epidemiology, etiology, pathological anatomy, prognosis, diagnosis, differential diagnosis, imaging and comprehensive therapy of each primary, relapsed, and metastasized tumor including surgery, chemo-, hormone- and radio- and targeted therapy. Another chapter is devoted to the prevention of subjecting sarcomas to inadequate surgical therapeutic measures under the assumed diagnosis of leiomyoma, and includes a diagnostic-therapeutic flowchart with a diagnostic score. The book aims to identify and provide diagnostic and therapeutic guidance. The listed tumor entities also constitute a particular diagnostic challenge for pathologists that contains numerous pitfalls and difficulties. This book, therefore, addresses gynecologists and pathologists in both clinical and private practice, but also surgeons and hemato-oncologists.