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1 edition of Non-vanishing of L-functions and applications found in the catalog.

# Non-vanishing of L-functions and applications

## by Maruti Ram Murty

Written in English

Edition Notes

The Physical Object ID Numbers Statement M. Ram Murty; V. Kumar Murty Series Modern Birkhäuser Classics Contributions Kumar Murty, V Pagination XI, 196 S. Number of Pages 196 Open Library OL27077728M ISBN 10 3034802730 ISBN 10 9783034802734 OCLC/WorldCa 799016250

Non-vanishing results for central values of L-functions in families have numerous applications, discovered, for example, in [4, 10, 12, 13, 25]. In particular, this paper is inspired by the work of Iwaniec and Sarnak [10], where they approached the problem of non-existence of Landau-Siegel zeros by studying the non-vanishing of automorphic L-. His research areas include number theory, modular forms, elliptic curves, and sieve theory. His book Non-vanishing of L-functions and Applications, coauthored by his brother V. Kumar Murty, won the Balaguer Prize and was published by Birkhauser.

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and Cited by: 8. Number Theory Books, P-adic Numbers, p-adic Analysis and Zeta-Functions, (2nd edn.)N. Koblitz, Graduate T Springer Algorithmic Number Theory, Vol. 1, E. Bach and J. Shallit, MIT Press, August ; Automorphic Forms and Representations, D. Bump, CUP ; Notes on Fermat's Last Theorem, A.J. van der Poorten, Canadian Mathematical Society .

2 automorphic L-functions 77 Adrian Diaconu and Dorian Goldfeld CM points and weight 3/2 modular forms Jens Funke The path to recent progress on small gaps between primes D. A. Goldston, J. Pintz, and C. Y. Yıldırım Negative values of truncations to L(1,χ) Andrew Granville and K. Soundararajan Long arithmetic progressions of. Bilinear forms with Kloosterman sums and applications Pages from Volume (), Issue 2 by Emmanuel Kowalski, Philippe Michel, Will Sawin AbstractCited by:

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### Non-vanishing of L-functions and applications by Maruti Ram Murty Download PDF EPUB FB2

This book systematically develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip. Researchers in number theory, graduate students who wish to enter into the area and non-specialists who wish to acquire an introduction to the subject will benefit by a study of this book.

The distri­ bution of prime numbers in arithmetic progressions is intimately connected with non-vanishing properties of various L-functions. With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical the­ Non-vanishing of L-functions and applications book have been shown to be equivalent to the non-vanishing of these L-functions on the line.

From the book reviews: “This is the softcover reprint of a monograph that was awarded the Ferran Sunyer i Balaguer prize in It is devoted to a recurring theme in number theory, namely that the non-vanishing of L-functions implies important arithmetical results.

Cited by: Non-vanishing of L-Functions and Applications. Summary: Develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip. This monograph brings together a collection of results on the non-vanishing of L­ functions.

The presentation, though based largely on the original papers, is suitable for independent study. A number of exercises have also been provided to aid in this endeavour. The exercises are of. Get this from a library. Non-vanishing of L-functions and applications.

[Maruti Ram Murty; Vijaya Kumar Murty] -- This book systematically develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip. Researchers in number theory, graduate students who wish to enter.

Award-winning monograph of the Ferran Sunyer i Balagure Prize This book systematically develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip. Researchers in number theory, graduate students who wish to enter into the area and non-specialists who wish to acquire an introduction to the subject will benefit by a study of this.

The distri- bution of prime numbers in arithmetic progressions is intimately connected with non-vanishing properties of various L-functions. With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical the- orems have been shown to be equivalent to the non-vanishing of these L-functions on the line.

Pris: kr. Häftad, Skickas inom vardagar. Köp Non-vanishing of L-Functions and Applications av M Ram Murty, V Kumar Murty på This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear by: Non-vanishing of modular L-functions corollary now follows from the Fundamental Lemma applied to the eigenform g z with d d F (note: s 0 u 0).

This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group.

and non-vanishing theorems, a thorough presentation of the explicit formulas of. new result concerning the nonvanishing of L-functions on. A different, highly geometric approach to the BSD conjecture for elliptic curves over function fields (via non-vanishing results for twists of L-functions) is proposed by Ulmer in [19].

As Author: Douglas Ulmer. Iwaniec and Kowalski sketch the argument in their book on analytic number theory, Corollary and the discussion preceding it, in pages They do not prove the non-vanishing of Hecke L-functions (but they give the statement, with a zero-free region) or Brauer's induction (but they reference Serre's book on representation theory).

Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois.

There is a theorem by Langlands and Shalika (link) that the L-function of a cuspidal automorphic representation does not vanish on the line $\mathrm{Re}(s)=1$. Central analytic questions about L-functions include their moments, size, non-vanishing, distribution of zeros and have been key to expanding our understanding of the distribution of prime numbers, arithmetic statistics, equidistribution of special points and periods, Diophantine equations, random matrix theory, and quantum chaos.

Inhe, along with his brother, M. Ram Murty, received the Ferran Sunyer i Balaguer Prize for the book "Non-vanishing of L-functions and their applications." Inthe Canadian Mathematical Society listed him in their inaugural class of fellows.

ReferencesAuthority control: BIBSYS:. The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory.

It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular. Advanced Analytic Number Theory: L-Functions is a broad introduction and survey of the theory of Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group GL approach is a generalization of the ideas of J.

Tate (Tate's thesis) and A. Weil, who used abstract harmonic .The purpose of this book is to give an exposition of the analytic theory of L- functions following the ideas of harmonic analysis inaugurated by Tate and Weil.

The central theme is the exploitation of the Local Langlands' Correspondence for.These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality.

InVoronin proved that any non-vanishing analytic function can be approximated uniformly by certain shifts of the Riemann zeta-function in the critical strip.