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
Let be a field of degree over , the field of rational -adic numbers, say with residue degree , ramification index and differential exponent . Let be the ring of integers of and its unique prime ideal. The trace and norm maps for are denoted and , respectively. Fix , a power of a prime , and let be a numerical character defined modulo and of order . The character extends to the ring of -adic integers in the natural way; namely , where denotes the residue class...
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.
Kloosterman sums in residue rings
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-Fourier inversion for symmetric matrices
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.
Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers