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The author tries to show the connection between number theory and other branches of mathematics with the resultant tools adopted in the book ranging from algebra to probability theory, but without exceeding the undergraduate students who wish to be acquainted with number theory, graduate students intending to specialize in this field and researchers requiring the present state of knowledge.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543574806818,"sku":"9789971950262-new","price":31.31,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789971950262.jpg?v=1776385214"},{"product_id":"jacobsthal-sums-9789819813162-new","title":"Jacobsthal Sums","description":"\u003cp\u003eThe focus of this monograph is on the Jacobsthal sums of the title. These are quadratic character sums with polynomial arguments of a certain simple form. 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Complete solutions to all exercises are provided.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis monograph should be of interest to researchers studying character sums or counting solutions to equations over finite fields, as well as to graduate students and advanced undergraduates interested in these topics.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543604855074,"sku":"9789819813162-new","price":82.27,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789819813162.jpg?v=1776386164"},{"product_id":"prime-numbers-friends-who-give-problems-9789814725811-new","title":"Prime Numbers, Friends Who Give Problems: A Trialogue with Papa Paulo","description":"\u003cp\u003e\u003cem\u003e\"This is a charming book, written as a conversation between mathematician Papa Paulo and his grandsons. A motivated reader can learn not only about prime numbers, but also something about how mathematicians think, work, and ask questions from reading this book.\"\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003eMathematical Association of America\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cem\u003ePrime Numbers, Friends Who Give Problems\u003c\/em\u003e is written as a trialogue, with two persons who are interested in prime numbers asking the author, Papa Paulo, intelligent questions. Starting at a very elementary level, the book advances steadily, covering all important topics of the theory of prime numbers, up to the most famous problems. The humorous conversations and the inclusion of a back-story add to the uniqueness of the book. 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It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research.\u003c\/p\u003e\u003cp\u003eThe book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their \u003cem\u003eq\u003c\/em\u003e-analogs and their finite versions (by taking partial sums modulo suitable prime powers). 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For example, the celebrated Gauss quadratic reciprocity law is proved in four independent ways, which are in some way or other dependent on the functional equation. The proofs rest on finite fields, representation theory of nilpotent groups, reciprocity law for the Dedekind sums, and the translation formula for the theta-series, respectively. Likewise, for example, the Euler function is treated in several different places.One of the important principles of learning is to work with the material many times. This book presents many worked-out examples and exercises to enhance the reader's comprehension on the topics covered in an in-depth manner. This is done in a different setting each time such that the reader will always be challenged. 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In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eIn this new second edition, a detailed description of Barsotti-Tate groups (including formal Lie groups) is added to Chapter 1. As an application, a down-to-earth description of formal deformation theory of elliptic curves is incorporated at the end of Chapter 2 (in order to make the proof of regularity of the moduli of elliptic curve more conceptual), and in Chapter 4, though limited to ordinary cases, newly incorporated are Ribet's theorem of full image of modular p-adic Galois representation and its generalization to 'big' Λ-adic Galois representations under mild assumptions (a new result of the author). Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian ℚ-varieties and ℚ-curves).\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543697195298,"sku":"9789814368643-new","price":175.8,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814368643.jpg?v=1776390004"},{"product_id":"figurate-numbers-9789814355483-new","title":"Figurate Numbers","description":"Figurate numbers have a rich history with many applications. The main purpose of this book is to provide a thorough and complete presentation of the theory of figurate numbers, giving much of their properties, facts and theorems with full proofs. 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There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. 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All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eIn each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. 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