Bounds and computational results for exponential sums related to cusp forms
The aim of this paper is to present some computer data suggesting the correct size of bounds for exponential sums of Fourier coefficients of holomorphic cusp forms.
Bounds for double zeta-functions
In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region .First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.
Bounds for exponential sums and their applications to pseudorandom numbers
Character sums in complex half-planes
Let be a finite subset of an abelian group and let be a closed half-plane of the complex plane, containing zero. We show that (unless possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of which belongs to . In other words, there exists a non-trivial character such that .
Cubic norms represented by quadratic sequences
Difference sets and the primes
Digital expansion of exponential sequences
We consider the -ary digital expansion of the first terms of an exponential sequence . Using a result due to Kiss and Tichy [8], we prove that the average number of occurrences of an arbitrary digital block in the last digits is asymptotically equal to the expected value. Under stronger assumptions we get a similar result for the first digits, where is a positive constant. In both methods, we use estimations of exponential sums and the concept of discrepancy of real sequences modulo ...
Distribution of consecutive modular roots of an integer
Distribution of difference between inverses of consecutive integers modulo .
Distribution of the power generator over a residue ring for parts of the period.
Distribution properties of digital expansions arising from linear recurrences
Eigenvalues in the large sieve inequality, II
We explore numerically the eigenvalues of the hermitian formwhen . We improve on the existing upper bound, and produce a (conjectural) plot of the asymptotic distribution of its eigenvalues by exploiting fairly extensive computations. The main outcome is that this asymptotic density most probably exists but is not continuous with respect to the Lebesgue measure.
Errata to “The Dirichlet series of : On an error term associated with its coefficients” (Acta Arith. 75 (1996), 39-69)
Estimates for complete multiple exponential sums
Estimation of exponential sums of polynomials of higher degrees II
Estimation of some exponential sums containing the fractional part function and some other "non-standard" exponential sums
Explicit constructions of extractors and expanders
Exponential sums and additive problems involving square-free numbers
Exponential sums involving the largest prime factor function
Exponential sums modulo prime powers