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In mathematics, van der Corput's method generates estimates for exponential sums. The method applies two processes, the van der Corput processes A and B which relate the sums into simpler sums which are easier to estimate. The processes apply to exponential sums of the form = (())
If the sum is of the form = ()where ƒ is a smooth function, we could use the Euler–Maclaurin formula to convert the series into an integral, plus some corrections involving derivatives of S(x), then for large values of a you could use "stationary phase" method to calculate the integral and give an approximate evaluation of the sum.
In mathematics, Turán's method provides lower bounds for exponential sums and complex power sums. The method has been applied to problems in equidistribution. The method applies to sums of the form = = where the b and z are complex numbers and ν runs over a range of integers.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value {} denotes the fractional part of () is a Bernoulli polynomial.
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
In mathematics, a Kloosterman sum is a particular kind of exponential sum.They are named for the Dutch mathematician Hendrik Kloosterman, who introduced them in 1926 [1] when he adapted the Hardy–Littlewood circle method to tackle a problem involving positive definite diagonal quadratic forms in four variables, strengthening his 1924 dissertation research on five or more variables.
5.3.3 Matrix exponential. 6 Sums of divergent series. ... Download as PDF; Printable version; ... it is also possible to treat power series as formal sums, meaning ...
A powerful general result is Weyl's criterion, which shows that equidistribution is equivalent to having a non-trivial estimate for the exponential sums formed with the sequence as exponents. For the case of multiples of a, Weyl's criterion reduces the problem to summing finite geometric series.