Book Review: Non-vanishing of L-functions and applications

Dorian Goldfeld

Type: Article

Publication Date: 1999-12-21

Citations: 2

DOI: https://doi.org/10.1090/s0273-0979-99-00851-4

Abstract

The theory of L-functions and analytic number theory goes back to 1837 when Dirichlet introduced the L-series [D, chapter 4] (Dirichlet series)(where χ is a character of the cyclic group (Z/qZ) * for a positive integer q) to prove that there are infinitely many primes congruent to a (mod q) provided a is coprime to q.The key step in Dirichlet's proof was showing that

Locations

Bulletin of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Book Review: Advanced analytic number theory: L-functions	2007	Stephen Gelbart
+	Dirichlet L-functions	1982	Kenneth Ireland Michael Rosen
+ PDF Chat	Non-vanishing of L-Functions and Applications	1997	M. Ram Murty V. Kumar Murty
+	Dirichlet L-functions	1990	Kenneth Ireland Michael Rosen
+	L-Functions	1989	Toshitsune Miyake
+	Dirichlet Series and L-Functions	2008
+ PDF Chat	Non-vanishing of L-Functions and Applications	1997	M. Ram Murty V. Kumar Murty
+ PDF Chat	Topics in Analytic Number Theory	1985
+	Zeroes of $L$-series in characteristic $p$	2006	David Goss
+ PDF Chat	Book Review: Elementary theory of $L$-functions and Eisenstein series	1997	Glenn Stevens
+	Character sums, L- functions and applications	2020
+	L-series and Dirichlet’s prime number theorem	2013
+	L-series and Dirichlet’s prime number theorem	2013
+	Lectures on p-adic L-functions	1972	健吉岩沢
+ PDF Chat	Nonvanishing of Dirichlet $L$-functions with smooth conductors	2024	Sun-Kai Leung
+	ZEROES OF L-SERIES IN CHARACTERISTIC p	2006	David Goss
+	p-adic L-functions and Bernoulli Numbers	1982	Lawrence C. Washington
+	The Complex L-Functions	1976	Serge Lang
+	Special Values of L-Series	1992	Rhonda L. Hatcher
+ PDF Chat	Special values of derivatives of certain $L$-functions	2024	Tapas Chatterjee Sonika Dhillon

Works That Cite This (2)

Action	Title	Year	Authors
+ PDF Chat	Geometric non-vanishing	2004	Douglas Ulmer
+ PDF Chat	The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology	2008	Nikolaos Diamantis Cormac O’Sullivan

Works Cited by This (6)

Action	Title	Year	Authors
+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec
+ PDF Chat	Zeros of Dirichlet $L$-functions	1992	R. Balasubramanian V. Kumar Murty
+ PDF Chat	Oscillations of Fourier coefficients of modular forms	1983	M. Ram Murty
+	Eisenstein series of 1/2-integral weight and the mean value of real DirichletL-series	1985	Dorian Goldfeld Jeffrey Hoffstein
+ PDF Chat	On some applications of automorphic forms to number theory	1996	Daniel Bump Solomon Friedberg Jeffrey Hoffstein
+	Fourier coefficients of modular forms of half-integral weight	1985	Winfried Kohnen