EuDML | Browse

Let $K$ be a field of degree $n$ over $Q_{p}$ , the field of rational $p$ -adic numbers, say with residue degree $f$ , ramification index $e$ and differential exponent $d$ . Let $O$ be the ring of integers of $K$ and $P$ its unique prime ideal. The trace and norm maps for $K / Q_{p}$ are denoted $T r$ and $N$ , respectively. Fix $q = p^{r}$ , a power of a prime $p$ , and let $η$ be a numerical character defined modulo $q$ and of order $o (η)$ . The character $η$ extends to the ring of $p$ -adic integers $ℤ_{p}$ in the natural way; namely $η (u) = η (\tilde{u})$ , where $\tilde{u}$ denotes the residue class...

Kloosterman sums in residue classes

Valentin Blomer, Djordje Milićević (2015)

Journal of the European Mathematical Society

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.

Kloosterman sums in residue rings

J. Bourgain, M. Z. Garaev (2014)

Acta Arithmetica

We generalize some of our previous results on Kloosterman sums [Izv. Mat., to appear] for prime moduli to general moduli. This requires establishing the corresponding additive properties of the reciprocal-set I¯¹ = {x¯¹: x ∈ I}, where I is an interval in the ring of residue classes modulo a large positive integer. We apply our bounds on multilinear exponential sums to the Brun-Titchmarsh theorem and the estimate of very short Kloosterman sums, hence generalizing our earlier work to the setting of...

Kloosterman sums with prime variable

Roger C. Baker (2012)

Acta Arithmetica

Kloosterman-Fourier inversion for symmetric matrices

Omer Offen (2005)

Bulletin de la Société Mathématique de France

We formulate a Kloosterman transform on the space of generalized Kloosterman integrals on symmetric matrices, and obtain an inversion formula. The formula is a step towards a fundamental lemma of the Jacquet type. At the same time it hints towards a conjectural relative trace formula identity, associated with the metaplectic correspondence.

Currently displaying 1 – 14 of 14

Page 1

Displaying 1 – 14 of 14

Kloosterman identities over a quadratic extension II

Kloosterman Sums and Fourier Coefficients of Cusp Forms.

Kloosterman sums and primitive elements in Galois fields

Kloosterman sums and the p-torsion of certain Jacobians.

Kloosterman sums as algebraic integers.

Kloosterman sums for Clifford algebras and a lower bound for the positive eigenvalues of the Laplacian for congruence subgroups acting on hyperbolic spaces.

Kloosterman sums for prime powers in P-adic fields

Kloosterman sums in residue classes

Kloosterman sums in residue rings

Kloosterman sums with prime variable

Kloosterman-Fourier inversion for symmetric matrices

Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers

Kongruenzen zwischen Koeffizienten trigonometrischer Reihen und Klassenzahlen quadratisch imaginärer Körper.

Kummer's calculation of Lp (1,...).

Currently displaying 1 – 14 of 14