Exponential sums with multiplicative coefficients.
Exponential sums with rational function entries
Exponentialsummen und Nullstellen von L-Reihen.
Gitterpunkte unter algebraischen Kurven.
Goldbach numbers in sparse sequences
We show that for almost all , the inequalityhas solutions with odd prime numbers and , provided . Moreover, we give a rather sharp bound for the exceptional set.This result provides almost-all results for Goldbach numbers in sequences rather thinner than the values taken by any polynomial.
Hyper-Kloosterman sums and estimation of exponential sums of polynomials of higher degrees
Incomplete exponential sums and incomplete residue systems for congruences
Kloosterman sums in residue classes
We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.
Large families of elliptic curve pseudorandom binary sequences
Lattice Points in Large Convex Bodies.
Lattice points in large convex bodies, II
L'octogone régulier et la signature des formes quadratiques entières non singulières
La formule généralisant la loi de réciprocité quadratique de Legendre et exprimant le reste par huit de la signature d'une forme quadratique entière non dégénérée à l'aide d'une somme de Gauss est attribuée par Milnor à Milgram, la faisant remonter à Braun. Le formalisme de Witt la réduit au cas de dimension 1 que Chandrasekharan attribue à Cauchy et Kronecker. Braun soulignait que les preuves de ces formules nécessitent des moyens d'analyse. Une propriété métrique de l'octogone...
Lp-bounds for spherical maximal operators on Zn.
We prove analogue statements of the spherical maximal theorem of E. M. Stein, for the lattice points Zn. We decompose the discrete spherical measures as an integral of Gaussian kernels st,ε(x) = e2πi|x|2(t + iε). By using Minkowski's integral inequality it is enough to prove Lp-bounds for the corresponding convolution operators. The proof is then based on L2-estimates by analysing the Fourier transforms ^st,ε(ξ), which can be handled by making use of the circle method for exponential sums. As a...
Mean square value of exponential sums related to representation of integers as sum of two squares
Mean square value of exponential sums related to the representation of integers as sums of squares
Mean value estimates for exponential sums and L-functions: a spectral theoretic approach.
Mean value estimates for exponential sums with applications to -functions
Mittelwerte von Hecke Polynomen.
Multiple exponential sums with monomials
Multiplicative functions over short segments