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Analytic Number Theory
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
Zeros of families of automorphic $L$-functions close to 1
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
Algebraic trace functions over the primes
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
The Large Sieve and its Applications: Arithmetic Geometry, Random Walks and Discrete Groups
The principle of the large sieve is illustrated with examples of group and conjugacy sieves, as well as those of discrete groups and probabilistic sieves.
Rankin-Selberg $L$-functions in the level aspect
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
Introduction and motivation The language of representation theory Variants Linear representations of finite groups Abstract representation theory of compact groups Applications of representations of
A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations
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.
Algebraic twists of modular forms and Hecke orbits
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
Kloosterman paths and the shape of exponential sums
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.
Analytic problems for elliptic curves
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