Kloosterman sums, elliptic curves, and irreducible polynomials with prescribed trace and norm
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 sums with prime variable
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
Knebusch-Milnor exact sequence and parity of class numbers
Kneser’s theorem for upper Banach density
Suppose is a set of non-negative integers with upper Banach density (see definition below) and the upper Banach density of is less than . We characterize the structure of by showing the following: There is a positive integer and a set , which is the union of arithmetic sequences [We call a set of the form an arithmetic sequence of difference and call a set of the form an arithmetic progression of difference . So an arithmetic progression is finite and an arithmetic sequence...
K-nombres de Pisot et de Salem
Knot cobordism and amphicheirality.
Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamoḡlu-Ikeda lift
Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k - n/2 + 1/2 for Γ₀(4), let f be the corresponding primitive form of weight 2k-n for SL₂(ℤ) under the Shimura correspondence, and Iₙ(h) the Duke-Imamoḡlu-Ikeda lift of h to the space of cusp forms of weight k for Spₙ(ℤ). Moreover, let be the first Fourier-Jacobi coefficient of Iₙ(h), and be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding to under the...
Koecher-Maaß-Series for Modular Forms of Quaternions.
Kolam indiens, dessins sur le sable aux îles Vanuatu, courbe de Sierpinski et morphismes de monoïde
Nous montrons que le tracé d’un kolam indien classique, que l’on retrouve aussi dans la tradition des dessins sur le sable aux îles Vanuatu, peut être engendré par un morphisme de monoïde. La suite infinie morphique ainsi obtenue est reliée à la célèbre suite de Prouhet-Thue-Morse, mais elle n’est -automatique pour aucun entier .
Kolyvagin's method for Chow groups of Kuga-Sato varieties.
Kombinatorik mit dem Computer: Klassifikationen und damit verwandte Figuren.
Kommutatoren und 2-Cohomologie p-adischer Quaternionenschiefkörper.
Kompaktifizierung des Humbertschen Fundamentalbereichs.
Komposition der binären quadratischen Formen relativ einer Grundform.