Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Arithmetical Aspects of the Large Sieve Inequality
 
Olivier Ramaré Université Lille 1, Lille, France
D. S. Ramana Harish-Chandra Research Institute, Allahabad, India
A publication of Hindustan Book Agency
Arithmetical Aspects of the Large Sieve Inequality
Softcover ISBN:  978-81-85931-90-6
Product Code:  HIN/36
List Price: $42.00
AMS Member Price: $33.60
Please note AMS points can not be used for this product
Arithmetical Aspects of the Large Sieve Inequality
Click above image for expanded view
Arithmetical Aspects of the Large Sieve Inequality
Olivier Ramaré Université Lille 1, Lille, France
D. S. Ramana Harish-Chandra Research Institute, Allahabad, India
A publication of Hindustan Book Agency
Softcover ISBN:  978-81-85931-90-6
Product Code:  HIN/36
List Price: $42.00
AMS Member Price: $33.60
Please note AMS points can not be used for this product
  • Book Details
     
     
    Hindustan Book Agency
    Volume: 362009; 210 pp
    MSC: Primary 11

    This book is an elaboration of a series of lectures given at the Harish–Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality which, when applied to the Farey dissection, will reveal connections between this inequality, the Selberg sieve and other less used notions such as pseudo-characters and the \(\Lambda_Q\)-function, as well as extend these theories.

    One of the leading themes of these notes is the notion of so-called local models that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun–Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues, and an equally novel one of the Vinogradov's Three Primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them new, like a sharp upper bound for the number of twin primes \(p\) that are such that \(p+1\) is squarefree. In the end the problem of equality in the large sieve inequality is considered, and several results in this area are also proved.

    A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

    Readership

    Graduate students and research mathematicians interested in number theory.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 362009; 210 pp
MSC: Primary 11

This book is an elaboration of a series of lectures given at the Harish–Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality which, when applied to the Farey dissection, will reveal connections between this inequality, the Selberg sieve and other less used notions such as pseudo-characters and the \(\Lambda_Q\)-function, as well as extend these theories.

One of the leading themes of these notes is the notion of so-called local models that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun–Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues, and an equally novel one of the Vinogradov's Three Primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them new, like a sharp upper bound for the number of twin primes \(p\) that are such that \(p+1\) is squarefree. In the end the problem of equality in the large sieve inequality is considered, and several results in this area are also proved.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students and research mathematicians interested in number theory.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.