Sums of Squares of Integers
Sums of Squares of Integers
Sums of Squares of Integers
Sums of Squares of Integers
Sums of Squares of Integers
Sums of Squares of Integers
Trending Bestseller

Sums of Squares of Integers

Carlos J. Moreno
No reviews yet Write a Review
Paperback / softback
05 September 2019
$166.32
In Stock: Ships in 7-9 Days
Hurry up! Current stock:
icon Share icon Share
Description  
Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares.
The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.
Customer reviews  

This product hasn't received any reviews yet. Be the first to review this product!

Write a Reviews
Flat Rate Shipping  
Easy Returns  
$166.32
In Stock: Ships in 7-9 Days
Hurry up! Current stock:
icon Share icon Share
Flat Rate Shipping  
Easy Returns  

Sums of Squares of Integers

$166.32

Description

Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares.
The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.

Customers Also Viewed

Discover your next great read at BookLoop, Australia's trusted online bookstore offering a vast selection of titles across various genres and interests. Whether you're curious about what's trending or searching for graphic novels that captivate, thrilling crime and mystery fiction, or exhilarating action and adventure stories, our curated collections have something for every reader. Delve into imaginative fantasy worlds or explore the realms of science fiction that challenge the boundaries of reality.

For those with a green thumb, our comprehensive range of gardening books provides insights and tips for all levels of enthusiasts. If you're aiming to enhance your financial acumen, our selection of finance, business, and management books offers valuable knowledge from industry experts. Craft lovers will appreciate our assortment of handicrafts, decorative arts, and crafts books, perfect for inspiring your next project. Engage your mind with our collection of hobbies, quizzes, and games books, or explore the mystical with our fortune-telling and divination guides.

Transportation aficionados can immerse themselves in our extensive transportation books, including detailed works on road and motor vehicles. Young readers are not left out, with a delightful array of picture books and early learning concepts designed to educate and entertain. Fans of contemporary narratives will find compelling stories in our contemporary fiction section. Embark on epic journeys with our fantasy and science fiction titles, or gain inspiration from real-life tales in our biographies and true stories collection. Health-conscious readers can explore our health and wholefood cooking books, focusing on specific diets and conditions.

Stay updated with the literary world by browsing our trending books, featuring the latest bestsellers and critically acclaimed works. Explore titles from popular brands like Minecraft, Pokemon, Star Wars, Bluey, Lonely Planet, ABIA award winners, Peppa Pig, and our specialized collection of ADHD books. At BookLoop, we are committed to providing a diverse and enriching reading experience for all.