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Martin Sleziak
Martin Sleziak
10:25 AM
new-tag A new tag trigonometric-sums was created by Shubhrajit Bhattacharya. The same user also created a tag-excerpt.
> The method of trigonometric sums is one of the general methods in analytic number theory. Two problems in number theory required for their solution the creation of the method of trigonometric sums: the problem of the distribution of the fractional parts of a polynomial, and the problem of representing a positive integer as the sum of terms of a specified type (additive problems of number theory). Vinogradov used this method to prove his famous theorem.
On MathOverflow there is a tag called trigonometric-sums, but it has rather inconsistent use.
We should keep an eye on tags with rather similar names, such as trigonometric-sums and trigonometric-series. (I guess some users might use this tag simply for any tag related to sums and trigonometry.)
There is a closely related tag called exponential-sum - in fact, it appears on both questions with the new tag.
5
Q: Why should $\sum_{m=1}^N e(\alpha m^3)$ be big for some $\alpha?$

PedroI'm going through a "circle method" proof of the fact that every large enough natural number $n$ is the sum of nine cubes. At some point a lot of control over the function $$f(\alpha)=\sum_{m=1}^N e(\alpha m^3)$$ is needed. Here $N=\lfloor n^{1/3}\rfloor$ and $e(z)=e^{2\pi i z}$. If we first stud...

number-theory analytic-number-theory exponential-sum trigonometric-sums
12
Q: A Nice Problem In Additive Number Theory

Shubhrajit Bhattacharya$\color{red}{\mathrm{Problem:}}$ $n\geq2$ is a given positive integer, and $a_1 ,a_2, a_3, \ldots ,a_n$ are all given integers that aren't multiples of $n$ and $a_1 + \cdots + a_n$ is also not a multiple of $n$. Prove there are at least $n$ different $(e_1 ,e_2, \ldots ,e_n ) \in \{0,1\}^n $ such...

number-theory elementary-number-theory inequality exponential-sum trigonometric-sums
Exponential sum
In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function e ( x ) = exp ⁡ ( 2 π i x ) . {\displaystyle e(x)=\exp(2\pi ix).\,} Therefore, a typical exponential sum may take the form ∑ n e (...
Those queries did not return any older occurrences of trigonometric-sums.
 

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