منابع مشابه
Weyl 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 and Atomic Energy Oscillations
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.
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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 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 کاملThe Limit Points of Weyl Sums and Other Continuous Cocycles
This paper examines the limit points of continuous Z-cocycles defined on a minimal dynamical system and taking values in an abelian metrisable group. This is motivated by and applied to the study of classical exponential series X^-i^"'" 6+nx) t 0 show, in particular, that if 0 is a transcendental number with liminfe^ ||^|| < oo, then for each x chosen from a dense Gd subset of [0,1], these part...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 1995
ISSN: 0213-2230
DOI: 10.4171/rmi/170