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Bounds and computational results for exponential sums related to cusp forms

Anne-Maria Ernvall-Hytönen, Arto Lepistö (2009)

Acta Mathematica Universitatis Ostraviensis

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

Isao Kiuchi, Yoshio Tanigawa (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region $0 \leq ℜ s_{j} < 1 (j = 1, 2)$ .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

Jürgen Eichenauer-Herrmann, Harald Niederreiter (1994)

Acta Arithmetica

Character sums in complex half-planes

Sergei V. Konyagin, Vsevolod F. Lev (2004)

Journal de Théorie des Nombres de Bordeaux

Let $A$ be a finite subset of an abelian group $G$ and let $P$ be a closed half-plane of the complex plane, containing zero. We show that (unless $A$ possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of $A$ which belongs to $P$ . In other words, there exists a non-trivial character $χ \in \hat{G}$ such that $\sum_{a \in A} χ (a) \in P$ .

Cubic norms represented by quadratic sequences

Jacek Pomykała (1993)

Colloquium Mathematicae

Difference sets and the primes

Imre Z. Ruzsa, Tom Sanders (2008)

Acta Arithmetica

Digital expansion of exponential sequences

Michael Fuchs (2002)

Journal de théorie des nombres de Bordeaux

We consider the $q$ -ary digital expansion of the first $N$ terms of an exponential sequence $a^{n}$ . 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 $c log N$ digits is asymptotically equal to the expected value. Under stronger assumptions we get a similar result for the first ${(log N)}^{\frac{3}{2} - ϵ}$ digits, where $ϵ$ is a positive constant. In both methods, we use estimations of exponential sums and the concept of discrepancy of real sequences modulo $1$ ...

Distribution of consecutive modular roots of an integer

Jean Bourgain, Igor E. Shparlinski (2008)

Acta Arithmetica

Distribution of difference between inverses of consecutive integers modulo $p$ .

Chan, Tsz Ho (2004)

Integers

Distribution of the power generator over a residue ring for parts of the period.

Edwin El-Mahassini (2008)

Revista Matemática Complutense

Distribution properties of digital expansions arising from linear recurrences

Mario Lamberger, Jörg M. Thuswaldner (2003)

Mathematica Slovaca

Eigenvalues in the large sieve inequality, II

Olivier Ramaré (2010)

Journal de Théorie des Nombres de Bordeaux

We explore numerically the eigenvalues of the hermitian form $\sum_{q \leq Q} \sum_{a mod^{*} q} {|\sum_{n \leq N} ϕ_{n} e (n a / q)|}^{2}$ when $N = \sum_{q \leq Q} φ (q)$ . 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 $ζ (s) ζ^{α} (s + 1) f (s + 1)$ : On an error term associated with its coefficients” (Acta Arith. 75 (1996), 39-69)

U. Balakrishnan, Y.-F. S. Pétermann (1999)

Acta Arithmetica

Estimates for complete multiple exponential sums

J. H. Loxton (2000)

Acta Arithmetica

Estimation of exponential sums of polynomials of higher degrees II

Yangbo Ye (2000)

Acta Arithmetica

Estimation of some exponential sums containing the fractional part function and some other "non-standard" exponential sums

Grigori Kolesnik (2003)

Acta Arithmetica

Currently displaying 21 – 40 of 169

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Displaying 21 – 40 of 169

Bounds and computational results for exponential sums related to cusp forms

Bounds for double zeta-functions

Bounds for exponential sums and their applications to pseudorandom numbers

Character sums in complex half-planes

Cubic norms represented by quadratic sequences

Difference sets and the primes

Digital expansion of exponential sequences

Distribution of consecutive modular roots of an integer

Distribution of difference between inverses of consecutive integers modulo $p$ .

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

Errata to “The Dirichlet series of $ζ (s) ζ^{α} (s + 1) f (s + 1)$ : 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

Currently displaying 21 – 40 of 169