Quasi-Diagonal Behaviour and Smooth Weyl Sums
نویسندگان
چکیده
منابع مشابه
Breaking classical convexity in Waring's problem: Sums of cubes and quasi-diagonal behaviour
The natural interpretation of even moments of exponential sums, in terms of the number of solutions of certain underlying diophantine equations, permits a rich interplay to be developed between simple analytic inequalities, and estimates for those even moments. This interplay is in large part responsible for the remarkable success enjoyed by the Hardy-Littlewood method in its application to num...
متن کاملSmooth biproximity spaces and P-smooth quasi-proximity spaces
The notion of smooth biproximity space where $delta_1,delta_2$ are gradation proximities defined by Ghanim et al. [10]. In this paper, we show every smooth biproximity space $(X,delta_1,delta_2)$ induces a supra smooth proximity space $delta_{12}$ finer than $delta_1$ and $delta_2$. We study the relationship between $(X,delta_{12})$ and the $FP^*$-separation axioms which had been introduced by...
متن کاملPerturbations of Weyl Sums
Write fk(α;X) = ∑ x6X e(α1x + . . . + αkx ) (k > 3). We show that there is a set B ⊆ [0, 1)k−2 of full measure with the property that whenever (α2, . . . , αk−1) ∈ B and X is sufficiently large, then sup (α1,αk)∈[0,1) |fk(α;X)| 6 X1/2+4/(2k−1). For k > 5, this improves on work of Flaminio and Forni, in which a Diophantine condition is imposed on αk, and the exponent of X is 1−2/(3k(k−1)).
متن کاملWeyl Sums and Atomic Energy Oscillations Weyl Sums and Atomic Energy Oscillations Page 2
We extend Van der Corput's method for exponential sums to study an oscillating term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.
متن کاملWeyl Sums for Quadratic Roots
The most powerful methods for handling these sums exploit the modern theory of automorphic forms; see [DFI1] for spectral aspects and [DIT] for more arithmetical connections. The sum (1.1) has only a few terms, bounded by the divisor function, so there is not much room for cancellation, but for applications there is a lot of interest in bounds for sums of these as the modulus c varies, say (1.2...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Monatshefte f�r Mathematik
سال: 2000
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s006050070045