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8m
reviewed Reviewed Expectation of product of cosines
5h
reviewed Close Using Excel's NormInv and Proportion Estimates for Monte Carlo
5h
reviewed Close Lower bound for sum of binomial coefficients without summation
8h
answered Estimate of the sum Taylor's coefficients
11h
comment A lower bound on the $L^2$ norm of a Dirichlet polynomial
It's a bit unclear to me what you're looking for. For example, consider a smoothed version (smooth the sum over $n$) of the example (and use Poisson summation). Seems to me that can be very small for all $T\le t\le 2T$.
20h
answered A lower bound on the $L^2$ norm of a Dirichlet polynomial
1d
reviewed Close How to solve the following integral
1d
comment Is every number the sum of two cubes modulo p where p is a prime not equal to 7?
@GjergjiZaimi: That's a nice idea (using that if $n$ is missed then so are all numbers of the form $nr^3$)! One would have to check that the cubes don't form an arithmetic progression, which indeed happens for $p=7$.
1d
comment Is every number the sum of two cubes modulo p where p is a prime not equal to 7?
In this case Hasse's theorem has a simpler proof: if one computes the number of points using additive characters you get $p-2$ plus the contribution from the Gauss sums attached to the two characters of order exactly $3$.
1d
awarded  Nice Answer
Oct
22
comment When are all sums of the elements of a set different?
In the additive combinatorics literature such sets are called ``dissociated".
Oct
22
reviewed Leave Closed A problem of a hacked article
Oct
22
reviewed Close Intuition behind $\zeta(2) = \frac{\pi^2}{6}$
Oct
21
reviewed Close Operations research and Linear Programming
Oct
20
reviewed Leave Open Who first defined quantum integers?
Oct
20
comment Lower bound of first moment of $L$-function on $\mathrm{GL}(3)$
Yes, this kind of lower bound in $t$-aspect is trivial for any $L$-function. The point is that you can approximate $L(\frac 12+it)$ by some long Dirichlet polynomial $\sum_{n\le T^{r}} a(n)n^{-1/2-it}$, say, with $a(1)=1$, and the $L$-function coming from $GL(r)$, say. If you now integrate with smooth weights $L(1/2+it)$ (without absolute values), then note that only the term $n=1$ contributes. The rest of the terms cancel out and are negligible for smooth weights (rapid decay of Fourier transforms). So the bound $\gg T$ follows.
Oct
19
reviewed Close is there an analogy between fractals and automorphic forms?
Oct
19
reviewed Close Where can I find the classification of groups of order 8p?
Oct
18
reviewed Close Bender's decomposition with overlapping y variables
Oct
18
revised Inequality for an integral involving $ \exp $, $ \sin $ and $ \cos $
edited body