Weyl sums and atomic energy oscillations

Antonio Cordóba, Charles Fefferman, Luis Seco

Type: Article

Publication Date: 1995-04-30

Citations: 8

DOI: https://doi.org/10.4171/rmi/170

Abstract

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.

Locations

Revista Matemática Iberoamericana - View - PDF

Similar Works

Action	Title	Year	Authors
+	A trigonometric sum relevant to the nonrelativistic theory of atoms.	1994	Antonio Córdoba Charles Fefferman Luis Seco
+	Weyl sums and atomic energy oscillations	2024	Antonio Cordóba
+	Oscillatory integrals and exponential sums	2023	Ben Krause
+	Norms of exponential sums	1977	S. K. Pichorides
+	Estimates of Weyl?s exponential sums for very small values of the variable	2004	Ekkehard Kr�tzel
+ PDF Chat	A mean-value theorem for exponential sums. Applications to Weyl's inequality	2023	Olivier Robert Patrick Sargos
+	Damped Oscillatory Integrals and Maximal Operators	2005	Isroil A. Ikromov
+	Feynman diagrams and large order estimates for the exponential anharmonic oscillator	1987	Stephen Breen
+ PDF Chat	Krein systems with oscillating potentials	2024	Pavel Gubkin
+	Exponential sums with a large second derivative	2013	M. N. Huxley Grigori Kolesnik
+	Exponential sums	1991
+	Theory of Small Oscillations	2007	Vladimir I. Arnold Valery Vasil'evich Kozlov А. И. Нейштадт
+	Theory of Small Oscillations	1997	V. I. Arnold V. V. Kozlov А. И. Нейштадт
+	Exponential sums. I: The methods of Weyl and van der Corput (chapter 3)	1994	Hugh L. Montgomery
+	Oscillatory integrals	1996	Yu. Safarov Dmitri Vassiliev
+ PDF Chat	Oscillating integrals and Newton polyhedra	2005	Jan Denef Johannes Nicaise Patrick Sargos
+	Exponential Operators	1967
+	Small values of Weyl sums	2020	Changhao Chen Igor E. Shparlinski
+	Damping oscillatory integrals	1990	Michael Cowling Shaun Disney Giancarlo Mauceri Detlef M�ller
+	Wave operators for oscillating potentials	1977	Martin Schechter

Works That Cite This (3)

Action	Title	Year	Authors
+	Ideas Behind Kolmogorov Complexity and Related Kolmogorov's Ideas about The Physical Impossibility of Large Integers: How Their Formalization Can Help in Foundations of Physics	2001	Isaak A. Kunin Владик Крейнович Yu. A. Kuperin
+	A number-theoretic estimate for the thomas-fermi density	1996	Córdoba Antonio L. Fefferman Antonio de Amescua Seco
+ PDF Chat	The Scott conjecture for large Coulomb systems: a review	2023	Rupert L. Frank Konstantin Merz Heinz Siedentop

Works Cited by This (0)

Action	Title	Year	Authors