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Around the Unit Circle
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way ...
A Genealogical and Biographical History of Allegheny County, Pennsylvania
The sketches in this book, numbering approximately 2,250 and naming a total of 50,000 related persons, generally treat subjects who were born in the early nineteenth century, with reference to immediate forebears of the late eighteenth century. The sketches typically mention the date and place of birth and marriage of the principal subject, the place of birth of his parents and often grandparents, sometimes the name of the first ancestor in America, and details of religion, education, military service, occupation, home, and residence.
