Huxley exponential sums curves
Web16 dec. 2004 · A Van der Corput exponential sum is $S = \Sigma \exp (2 \pi i f (m))$, where $m$ has size $M$, the function $f (x)$ has size $T$ and $\alpha = (\log M) / \log T … Web12 dec. 2024 · Exponential sums have the form \begin {equation*} S = \sum _ { n \in A } e ^ { 2 \pi i f ( n ) }, \end {equation*} where $A$ is a finite set of integers and $f$ is a real-valued function (cf. also Trigonometric sum ). The basic problem is to show, under suitable circumstances, that $S = o ( \# A )$ as $\# A \rightarrow \infty$.
Huxley exponential sums curves
Did you know?
Web16 dec. 2004 · A Van der Corput exponential sum is $S = \Sigma \exp (2 \pi i f (m))$, where $m$ has size $M$, the function $f (x)$ has size $T$ and $\alpha = (\log M) / \log T < 1$. There are different bounds for $S$ in different ranges for $\alpha $. In the middle range where $\alpha $ is near $ {1\over 2}$, $S = O (\sqrt {M} T^ {\theta + \epsilon })$. WebExponential Sums and Lattice Points . × Close Log In. Log in with Facebook Log in with Google. or. Email. Password. Remember me on this computer. or reset password. Enter the email ... Martin N Huxley. 1993, Proceedings of the London Mathematical Society. Continue Reading. Download Free PDF.
Web13 jun. 1996 · This book is a thorough treatment of the developments arising from the method developed by Bombieri and Iwaniec in 1986 for estimating the Riemann zeta … WebEstimating an exponential sum with phase function f (x) is like the lattice point problem for the underlying curve y = f' (x). Resonances occur when an affine map that fixes the integer lattice superposes one arc of the underlying curve onto …
WebM.N. Huxley (1996a), Area, Lattice Points and Exponential Sums, London Math. Soc. Monographs 13 (Oxford University Press). Google Scholar M.N. Huxley (1996b), “The … WebEXPONENTIAL SUMS WITH A PARAMETER M. N. HUXLEY and N. WATT [Received 12 August 1988—Revised 6 December 1988] ABSTRACT Let F(x,y) be a real function with sufficiently many derivatives existing and satisfying certain non-vanishing conditions for 1 ^ …
Web23 okt. 2003 · This paper sets up an iteration step from a strong hypothesis about integer points close to curves to a bound for the discrepancy, the number of integer points minus the area, as in the latest work on single exponential sums.
WebM.N. Huxley (1996b), “The integer points close to a curveII”inAnalytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam 2, 487–516 ( Birkhäuser, Boston ). Google Scholar M.N. Huxley, “The integer points close to a curve III”in Number Theory in Progress I1(1999), 911–940 (de Gruyter, Berlin). Google Scholar is denver public schools closed todayhttp://mathsdemo.cf.ac.uk/maths/research/researchgroups/numbertheory/exponential/index.html is denver safe cityWeb23 dec. 2016 · Abstract A Van der Corput exponential sum is S = Σ exp (2 π i f ( m )) where m has size M, the function f ( x) has size T and α = (log M) / log T < 1. There are … is denver seminary conservativeWebThe work of Huxley in [H1] (resp. [H2]) produced the exponents 89 570 = 0.15614...and 32 205 = 0.15609..., resp 2 while our A6-bound leads to the exponent13 84= 0.15476..., hence doubling the saving over1 6obtained in [B-I1]. In §5 we highlight a new exponent pair that results from our work. is denver in central timerws writing mentorsWeb22 aug. 1996 · Huxley and his coworkers have taken this method and vastly extended and improved it. Area, Lattice Points, and Exponential Sums - M. N. Huxley - Oxford … is denver nc in lincoln countyWeb23 dec. 2016 · This paper sets up an iteration step from a strong hypothesis about integer points close to curves to a bound for the discrepancy, the number of integer points minus … rws.lunch room.de