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# đŸ“™ Arithmetical Aspects of the Large Sieve Inequality by Olivier RamarĂ©, D.S. Ramana â€” epub download

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This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute in February~2005. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\Lambda_Q$-function, as well as extend these theories.
One of the leading theme of these notes is the notion of so-called local models that throws a unifying light on the subject. As examples and applications, we 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 three primes Theorem; we also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes p that are such that p+1 is squarefree. We end our journey by considering the problem of equality in the large sieve inequality and prove several results in this area.

## About book:

## About file:

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- Series:
**HRI Lecture Notes in Mathematics** - Author:
**Olivier RamarĂ©, D.S. Ramana** - Year:
**2009** - Publisher:
**Hindustan Book Agency** - Language:
**English** - ISBN:
**978-8185931906**

- File size:
**1 202 220** - Format:
**pdf**

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Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying princi...

Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying princi...

A number of eminent mathematicians were invited to Bielefeld, Germany in 1999 to present lectures at a conference on topological, combinatorial and arithmetic aspects of (infinite) groups. The present volume consists of survey and research articles invite...

A number of eminent mathematicians were invited to Bielefeld, Germany in 1999 to present lectures at a conference on topological, combinatorial and arithmetic aspects of (infinite) groups. The present volume consists of survey and research articles invite...

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the ...

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the ...

Short but sweet -- by far the best introduction to the subject, which might prepare you for the firehose that is The Large Sieve and its Applications: Arithmetic Geometry, Random Walks and Discrete Groups (Cambridge Tracts in Mathematics)...

The theory of continued fractions has been defined by a small handful of books. This is one of them. The focus of Wall's book is on the study of continued fractions in the theory of analytic functions, rather than on arithmetical aspects. There are extend...

For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic 3-manifolds (and Kleinian groups), as these manifolds form the large...