{"product_id":"function-field-arithmetic-clear-exposition-of-modern-topics","title":"Function Field Arithmetic - Clear Exposition of Modern Topics","description":"\u003cp\u003eIn this review of Function field arithmetic the bottom line is straightforward: this is a focused, workmanlike graduate-level text best suited to researchers and advanced students who already know the basics of global fields and want a modern exposition linking Drinfeld modules, transcendence, and diophantine questions. The book's single biggest reason to buy is its emphasis on recent developments and worked examples that connect classical structures to new topics such as multizeta values and log-algebraicity, making it a useful reference rather than an introductory textbook.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n \u003cli\u003e\n\u003cstrong\u003eRecent developments:\u003c\/strong\u003e Presents up-to-date material on Drinfeld modules and related advances so readers encounter contemporary research directions rather than only classical theory.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eTranscendence focus:\u003c\/strong\u003e Explains the arithmetic of special values of transcendental functions, offering insight into zeta and gamma analogues and their interpolations that are central to current work.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eDiophantine approximation:\u003c\/strong\u003e Covers diophantine approximation and open problems, providing statements and context that stimulate further study and research questions.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eWorked examples:\u003c\/strong\u003e Includes numerous worked-out examples that help readers bridge abstract theory to concrete computations and heuristics.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eComplementary scope:\u003c\/strong\u003e Complements earlier foundational texts by treating new topics such as hypergeometric functions, modular forms, automata, and solitons in the function field setting.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis book is aimed at graduate students, postdocs and researchers in number theory or arithmetic geometry who already have a grounding in global fields and seek a concise, modern treatment of function field topics. Those working on transcendence, multizeta values, or Drinfeld modules will find the focused exposition and examples directly relevant to research.\u003c\/p\u003e\n\u003cp\u003eIt is not aimed at beginners encountering algebraic number theory for the first time; readers who need a slow, introductory presentation should consult more basic texts before approaching this volume, as the treatment assumes familiarity with key structures.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n \u003cli\u003eConcentrated coverage of recent research makes it a practical reference for specialists in function field arithmetic.\u003c\/li\u003e\n \u003cli\u003eMultiple worked examples clarify complicated ideas and demonstrate methods in practice.\u003c\/li\u003e\n \u003cli\u003eInclusion of newer topics such as multizeta values and log-algebraicity broadens the standard curriculum.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n \u003cli\u003eThe text assumes prior background and so is not suitable as a first introduction to algebraic or analytic number theory.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n \u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eFunction field arithmetic\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eDinesh S. Thakur\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eSubject focus\u003c\/td\u003e\n\u003ctd\u003eDrinfeld modules, transcendence, diophantine approximation\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eContent highlights\u003c\/td\u003e\n\u003ctd\u003eMultizeta values, log-algebraicity, hypergeometric and modular forms\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eIncludes\u003c\/td\u003e\n\u003ctd\u003eNumerous worked examples and discussion of open problems\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eTarget audience\u003c\/td\u003e\n\u003ctd\u003eAdvanced students and researchers in pure mathematics\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eFunction field arithmetic is a valuable, up-to-date reference for readers already comfortable with algebraic and arithmetic foundations; its emphasis on recent developments, worked examples and new topics like multizeta values makes it good value for researchers seeking a concise synthesis rather than a beginner text.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eIs this book suitable for beginners?\u003c\/strong\u003e\u003cbr\u003eNo. The book assumes prior knowledge of global fields and related algebraic structures and is best after introductory courses.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it include worked examples?\u003c\/strong\u003e\u003cbr\u003eYes. The author has included numerous worked-out examples to illustrate techniques and computations.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it cover modern research topics?\u003c\/strong\u003e\u003cbr\u003eYes. It addresses recent developments such as multizeta values, log-algebraicity, and the arithmetic of transcendental function values.\u003c\/p\u003e","brand":"Dinesh S. Thakur","offers":[{"title":"Default Title","offer_id":48636724510939,"sku":"9812388397","price":181.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51qqmfmGzgL._SL1360.jpg?v=1778598439","url":"https:\/\/gearmusthave.com\/products\/function-field-arithmetic-clear-exposition-of-modern-topics","provider":"GearMustHave","version":"1.0","type":"link"}