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Analytic Number Theory

- H. Iwaniec, E. Kowalski
- Mathematics
- 2004

Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of $L$-functions Elementary sieve methods Bilinear forms and the large… Expand

Zeros of families of automorphic $L$-functions close to 1

- E. Kowalski, P. Michel
- Mathematics
- 1 December 2002

For many L-functions of arithmetic interest, the values on or close to the edge of the region of absolute convergence are of great importance, as shown for instance by the proof of the Prime Number… Expand

Algebraic trace functions over the primes

- 'Etienne Fouvry, E. Kowalski, P. Michel
- Mathematics
- 26 November 2012

We study sums over primes of trace functions of l-adic sheaves. Using an extension of our earlier results on algebraic twists of modular forms to the case of Eisenstein series and bounds for Type II… Expand

The Large Sieve and its Applications: Arithmetic Geometry, Random Walks and Discrete Groups

- E. Kowalski
- Mathematics, Computer Science
- 2008

TLDR

Rankin-Selberg $L$-functions in the level aspect

- E. Kowalski, P. Michel, J. Vanderkam
- Economics, Education
- 15 July 2002

Keywords: moments ; Rankin-Selberg convolution ; level aspect ; convexity-breaking Reference TAN-ARTICLE-2002-003doi:10.1215/S0012-7094-02-11416-1 Record created on 2008-11-14, modified on 2017-05-12

An Introduction to the Representation Theory of Groups

- E. Kowalski
- Mathematics
- 28 August 2014

Introduction and motivation The language of representation theory Variants Linear representations of finite groups Abstract representation theory of compact groups Applications of representations of… Expand

A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations

- W. Duke, E. Kowalski
- Mathematics
- 2000

and the (weaker) conjecture n q for all ε > 0 is known as Vinogradov’s conjecture. Linnik’s technique makes it possible to prove that the number of exceptions to these conjectures is extremely small.… Expand

Algebraic twists of modular forms and Hecke orbits

- É. Fouvry, E. Kowalski, P. Michel
- Mathematics
- 3 July 2012

We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a… Expand

Kloosterman paths and the shape of exponential sums

- E. Kowalski, W. Sawin
- MathematicsCompositio Mathematica
- 29 October 2014

We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums $\text{Kl}_{p}(a)$ , as $a$ varies over $\mathbf{F}_{p}^{\times }$ and as $p$ tends to infinity.… Expand

Analytic problems for elliptic curves

- E. Kowalski
- Mathematics
- 10 October 2005

We consider some problems of analytic number theory for elliptic curves which can be considered as analogues of classical questions around the distribution of primes in arithmetic progressions to… Expand

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