The Fourier coefficients of modular forms are of widespread interest as an important source of arithmetic information. In many cases, these coefficients can be recovered from explicit knowledge of the traces of Hecke operators. The original trace formula for Hecke operators was given by Selberg in 1956. Many improvements were made in subsequent years, notably by Eichler and Hijikata. This book provides a comprehensive modern treatment of the Eichler-Selberg/Hijikata trace formulafor the traces of Hecke operators on spaces of holomorphic cusp forms of weight $\mathtt{k >2$ for congruence subgroups of $\operatorname{SL 2(\mathbf{Z )$. The first half of the text brings together the background from number theory and representation theory required for the computation. Thisincludes detailed discussions of modular forms, Hecke operators, adeles and ideles, structure theory for $\operatorname{GL 2(\mathbf{A )$, strong approximation, integration on locally compact groups, the Poisson summation formula, adelic zeta functions, basic representation theory for locally compact groups, the unitary representations of $\operatorname{GL 2(\mathbf{R )$, and the connection between classical cusp forms and their adelic counterparts on $\operatorname{GL 2(\mathbf{A )$. Thesecond half begins with a full development of the geometric side of the Arthur-Selberg trace formula for the group $\operatorname{GL 2(\mathbf{A )$. This leads to an expression for the trace of a Hecke operator, which is then computed explicitly. The exposition is virtually self-contained, withcomplete references for the occasional use of auxiliary results. The book concludes with several applications of the final formula.
Dr Ayton has transformed understanding of Edward III's armies - compulsory reading for anyone interested in the Hundred Years War. WAR IN HISTORY [Michael Prestwich] The mounted, armoured knight is one of the most potent symbols of medieval civilisation; indeed, for much of the middle ages the armoured warhorse was what defined a man as a member of the military class. However, despite the status of the knightly warrior in medieval society, the military service of the later medieval English aristocracy remains an unaccountably neglected subject, and the warhorse itself has never attracted a major study based upon archival sources. This book seeks to open up new fields of research: it focuses on the horse inventories, documents which offer detailed lists of men-at-arms and their appraised warhorses, the valuation of which is a measure of its owner's social and military status. Dr Ayton is primarily concerned with the inventories and related records for Edward III's reign, a period which witnessed significant changes in the organisation of the English fighting machine. Thedocuments produced during this period of `military revolution' cast valuable light on the character and attitudes of the aristocratic military community at a time when its traditional role was in the course of re-evaluation. Dr ANDREW AYTON is senior lecturer in history at the University of Hull.
If the railroads won the Gilded Age, the coal industry lost it. Railroads epitomized modern management, high technology, and vast economies of scale. By comparison, the coal industry was embarrassingly primitive. Miners and operators dug coal, bought it, and sold it in 1900 in the same ways that they had for generations. In the popular imagination, coal miners epitomized anti-modern forces as the so-called “Molly Maguire” terrorists. Yet the sleekly modern railroads were utterly dependent upon the disorderly coal industry. Railroad managers demanded that coal operators and miners accept the purely subordinate role implied by their status. They refused. Fueling the Gilded Age shows how disorder in the coal industry disrupted the strategic plans of the railroads. It does so by expertly intertwining the history of two industries—railroads and coal mining—that historians have generally examined from separate vantage points. It shows the surprising connections between railroad management and miner organizing; railroad freight rate structure and coal mine operations; railroad strategy and strictly local legal precedents. It combines social, economic, and institutional approaches to explain the Gilded Age from the perspective of the relative losers of history rather than the winners. It beckons readers to examine the still-unresolved nature of America’s national conundrum: how to reconcile the competing demands of national corporations, local businesses, and employees.
Crusading and the Crusader States explores how the idea of holy war emerged from the troubled society of the eleventh century, and why Jerusalem and the Holy Land were so important to Europeans. It follows the progress of the major crusading expeditions, offering insights into initial success and subsequent failure, charts the development of new attitudes towards Islam and its followers, and shows the effects of the Crusades on society and culture in the Near East. Providing analysis and discussion of this vital period of medieval history, Andrew Jotischky discusses key questions such as how crusading evolved in theory and practice, how crusading expeditions were planned and carried out, why they were considered such an essential part of medieval society, and why their popularity endured despite military failures. This new edition takes into account the wealth of rich and varied recent research to show why crusading should be seen as central to the European experience in the Middle Ages. It engages with key historiographical debates of the past decade, including how Crusades were formed, the political culture and social networks of crusading, and the effects of crusading on western religious and aristocratic culture. It now extends into the fifteenth century to discuss the lasting ramifications of the Crusades, and illustrate their legacy into the early modern period. It is essential reading for all students of the Crusades and medieval history.
Unlike traditional references that recount political and military history, this encyclopedia includes entries on a wide range of aspects related to daily life during the medieval crusades. The medieval crusades were fundamental in shaping world history and provide background for the conflict that exists between the West and the Muslim world today. This two-volume set presents fundamental information about the medieval crusades as a movement and its ideological impact on both the crusaders and the peoples of the East. It takes a broad look at numerous topics related to crusading, with the goal of helping readers to better understand what inspired the crusaders, the hardships associated with crusading, and how crusading has influenced the development of cultures both in the East and the West. The first of the two thematically arranged volumes considers topics such as the arts, economics and work, food and drink, family and gender, and fashion and appearance. The second volume considers topics such as housing and community, politics and warfare, recreation and social customs, religion and beliefs, and science and technology. Within each topical section are alphabetically arranged reference entries, complete with cross-references and suggestions for further reading. Selections from primary source documents, each accompanied by an introductory headnote, give readers first-hand accounts of the crusades.
The book investigates a riveting, richly documented conflict from thirteenth-century England over church property and ecclesiastical patronage. Oliver Sutton, the bishop of Lincoln, and John St. John, a royal household knight, both used coveted papal provisions to bestow the valuable church of Thame to a familial clerical candidate (a nephew and son, respectively). Between 1292 and 1294 three people died over the right to possess this church benefice and countless others were attacked or publicly scorned during the conflict. More broadly, religious services were paralyzed, prized animals were mutilated, and property was destroyed. Ultimately, the king personally brokered a settlement because he needed his knight for combat. Employing a microhistorical approach, this book uses abundant episcopal, royal, and judicial records to reconstruct this complex story that exposes in vivid detail the nature and limits of episcopal and royal power and the significance and practical business of ecclesiastical benefaction. This volume will appeal to undergraduate and graduate students alike, particularly students in historical methods courses, medieval surveys, upper-division undergraduate courses, and graduate seminars. It would also appeal to admirers of microhistories and people interested in issues pertaining to gender, masculinity, and identity in the Middle Ages.
This study of Sir Thomas Malory's Le Morte Darthur centres on its main narrative interest, armed combat. The description of knightly combat, with its complex thematic affinities, is seen as Malory's chief expressive medium. In the analysis of the discourse of fighting, some repeated descriptive preoccupations - to do with name, vision, blood, emotion and gesture - are treated as 'needs of meaning' with relevance for the whole text, and related to political, religious, genealogical, sexual and medical views of Malory's period. The critical discussion thus rests more on these elements of discourse rather than on the broader concepts such as 'chivalry' or 'love' normally applied to Malory.
The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.
An essential part of the library for anyone interested in the great political and military upheavals in the 15th century.' – Graeme Rimer, Retired Former Academic Director of the Royal Armouries 'A creditable effort to examine a neglected aspect of medieval warfare.' – Jim Bradbury, Cambridge University Press 'Everything you need to know about being a soldier in the Wars of the Roses.' – The Mail Bookshop What was it like to fight in a Wars of the Roses battle? What kind of men fought at St Albans, Northampton, Wakefield, Towton, Tewkesbury and Bosworth? How was the medieval soldier recruited, paid, equipped, fed and billeted? And how was a battle contested once both sides resorted to all-out conflict? First published in 1998, this classic study of the medieval soldier in the Wars of the Roses examines these and other questions using various documentary sources and recent evidence. Eyewitness accounts, contemporary chronicles, personal letters, civic records, archaeology and surviving military equipment are used to paint a fascinating picture of the medieval soldier. Evidence gleaned from the mass war grave found close to the battlefield of Towton in North Yorkshire sheds new light on those that lived and died in the civil wars. But what do we know about the psychology of those involved? And how did soldiers feel about killing their fellow Englishmen? Andrew Boardman explores the grim reality of medieval soldiering on land and sea during this crucial period of aristocratic violence and dynastic upheaval. He makes us question the current historical record, such as it is, and our perceptions of chivalry and warfare in Lancastrian and Yorkist England. The text is supported by many contemporary illustrations, diagrams and maps, making this updated work an indispensable guide to medieval soldiering in the late fifteenth century.
Andrew Lang, assisted by Walter Leaf and Ernest Myers, has put the old Greek epos into contemporary English prose. The subject of the Iliad, as the first line proclaims, is the “anger of Achilles.” The manner in which this subject is worked out will appear from the following summary in which we distinguish (1) the plot, i.e. the story of the quarrel, (2) the main course of the war, which forms a sort of underplot, and (3) subordinate episodes.
This collection represents some of the best recent critical writing on Edmund Spenser, a major Renaissance English poet. The essays cover the whole of Spensers work, from early literary experiments such as The Shepeardes Calendar, to his unfinished crowning work,The Fairie Queene. The introduction provides an overview of critical responses to Spenser, setting his work and the debates which it has generated in their perspective contexts: new historicist, post-structural, psychoanalytic and feminist. His study also covers the critical responses of leading British, Irish and American scholars.
In American fiction, two forms of the Arthurian myth are commonly found: the use of the myth for political reasons, and the use of the myth for the continuation of an aesthetic tradition that can be traced back to the earliest use of the Arthurian cycle by writers in the British Isles. This work traces the use of the legend from Mark Twain's A Connecticut Yankee in King Arthur's Court to Donald Barthelme's novel The King. It discusses how Twain used the myth to take a stand against England, how it served cultural and aesthetic purposes in John Steinbeck's writing, how Raymond Chandler used it in complex texts with less obvious Arthurian allusions that carried strong cultural and even political associations, how John Gardner used aspects of the myth to embellish already existing narrative structures and to underscore philosophic debates, and how Donald Barthelme suggests the continuing interest of American writers in the Arthurian legend today in his novels. Also discussed is the effect of World War II on American literature and the Arthurian myth and the Camelot image surrounding the Kennedys.
Dr Ayton has transformed understanding of Edward III's armies - compulsory reading for anyone interested in the Hundred Years War. WAR IN HISTORY [Michael Prestwich] The mounted, armoured knight is one of the most potent symbols of medieval civilisation; indeed, for much of the middle ages the armoured warhorse was what defined a man as a member of the military class. However, despite the status of the knightly warrior in medieval society, the military service of the later medieval English aristocracy remains an unaccountably neglected subject, and the warhorse itself has never attracted a major study based upon archival sources. This book seeks to open up new fields of research: it focuses on the horse inventories, documents which offer detailed lists of men-at-arms and their appraised warhorses, the valuation of which is a measure of its owner's social and military status. Dr Ayton is primarily concerned with the inventories and related records for Edward III's reign, a period which witnessed significant changes in the organisation of the English fighting machine. Thedocuments produced during this period of `military revolution' cast valuable light on the character and attitudes of the aristocratic military community at a time when its traditional role was in the course of re-evaluation. Dr ANDREW AYTON is senior lecturer in history at the University of Hull.
The first full commentary on Piers Plowman since the late nineteenth century is inaugurated with the publication of the first two of its five projected volumes.
A major new study piecing together the intriguing but fragmentary evidence surrounding the lives of minstrels to highlight how these seemingly peripheral figures were keenly involved with all aspects of late medieval communities. Minstrels were a common sight and sound in the late Middle Ages. Aristocrats, knights and ladies heard them on great occasions (such as Edward I's wedding feast for his daughter Elizabeth in 1296) and in quieter moments in their chambers; town-dwellers heard and saw them in civic processions (when their sound drew attention to the spectacle); and even in the countryside people heard them at weddings, church-ales and other parish celebrations. But who were the minstrels, and what did they do? How did they live, and how easily did they make a living? How did they perform, and in what conditions? The evidence is intriguing but fragmentary, including literary and iconographic sources and, most importantly, the financial records of royal and aristocratic households and of towns. These offer many insights, although they are often hard to fit into any coherent picture of the minstrels' lives and their place in society. It is easy to see the minstrels as peripheral figures, entertainers who had no central place in the medieval world. Yet they were full members of it, interacting with the ordinary people around them, as well as with the ruling classes: carrying letters and important verbal messages, some lending huge sums of money to the king (to finance Henry V's Agincourt campaign in 1415, for instance), some regular and necessary civic servants, some committing crimes or suffering the crimes of others. In this book Rastall and Taylor bring to bear the available evidence to enlarge and enrich our view of the minstrel in late medieval society.
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