{"product_id":"modular-forms-basics-and-beyond-advanced-text-for-researchers","title":"Modular Forms: Basics and Beyond - Advanced Text for Researchers","description":"\u003cp\u003eIn this review of Modular Forms: Basics and Beyond the bottom line is simple: this is a book for mathematically mature readers who already know the elementary theory and want a focused, deeper treatment. The reviewer finds the book valuable because it presents every definition and essential fact for classical modular forms of one variable while moving quickly to less common material, notably \u003cstrong\u003emodular forms of half-integral weight\u003c\/strong\u003e and a systematic development of theta functions and Eisenstein series. It is not an introductory textbook for beginners but a compact, rigorous monograph for advanced students and researchers.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eComprehensive definitions:\u003c\/strong\u003e Every definition and essential fact about classical modular forms of one variable is stated so the reader can follow advanced developments without assuming missing background.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eHalf-integral weight theory:\u003c\/strong\u003e A principal new feature is the clear presentation of modular forms of half-integral weight, which expands tools available to researchers in the field.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eTheta function coverage:\u003c\/strong\u003e The book treats theta functions systematically, linking classical constructions to later applications in the text.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eEisenstein series discussion:\u003c\/strong\u003e Both holomorphic and nonholomorphic Eisenstein series are discussed, giving a broader perspective than many elementary treatments.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eCompact monograph format:\u003c\/strong\u003e As a Springer Monograph, it is tightly written for readers who want concentrated theory rather than extended pedagogy.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis book suits graduate students, postdocs, and researchers in number theory or automorphic forms who already understand basic modular form concepts and want to learn advanced topics systematically. The reviewer recommends it to readers seeking a concise source that covers half-integral weights and theta\/Eisenstein series in one place.\u003c\/p\u003e\n\u003cp\u003eIt is not ideal for those new to modular forms or for self-learners without prior coursework in complex analysis and basic modular form theory; such readers should start with more elementary introductions before attempting this monograph.\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\u003eConcise presentation that gathers essential classical results and advanced topics in a single volume.\u003c\/li\u003e\n\u003cli\u003eIntroduces \u003cstrong\u003ehalf-integral weight\u003c\/strong\u003e theory in a way rarely found in elementary texts.\u003c\/li\u003e\n\u003cli\u003eSystematic treatment of theta functions and Eisenstein series broadens applicability to research problems.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eNot intended as an elementary textbook; readers without a solid background may struggle with the pace and density.\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\u003eModular Forms: Basics and Beyond\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eSpringer Monographs in Mathematics\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eGoro Shimura\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eScope\u003c\/td\u003e\n\u003ctd\u003eClassical modular forms of one variable; half-integral weight; theta and Eisenstein series\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAudience\u003c\/td\u003e\n\u003ctd\u003eAdvanced students and researchers in mathematics\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eModular Forms: Basics and Beyond is a compact, rigorous monograph that repays close study by readers who already know the basics. Its focused treatment of \u003cstrong\u003ehalf-integral weight\u003c\/strong\u003e forms and systematic discussion of theta and Eisenstein series make it good value for graduate students and researchers wanting a single reference on these advanced topics.\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 presumes familiarity with elementary modular form theory and complex analysis; beginners should consult introductory texts first.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it cover nonholomorphic Eisenstein series?\u003c\/strong\u003e\u003cbr\u003eYes. The monograph discusses both holomorphic and nonholomorphic Eisenstein series as part of its broader treatment.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWill this help with research in automorphic forms?\u003c\/strong\u003e\u003cbr\u003eYes. The systematic coverage of half-integral weights and theta functions provides tools and references useful for research in related areas.\u003c\/p\u003e","brand":"Goro Shimura","offers":[{"title":"Default Title","offer_id":48614096371931,"sku":"148999355X","price":125.37,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/61iOf2RqpqL._SL1208.jpg?v=1778375830","url":"https:\/\/gearmusthave.com\/products\/modular-forms-basics-and-beyond-advanced-text-for-researchers","provider":"GearMustHave","version":"1.0","type":"link"}