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Results tagged with nt.number-theory
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user 2900
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
1
vote
0
answers
155
views
partial sums of fractional parts
I'd like to bound the partial sum: $S(p,q,\alpha):=\sum\limits^{p+q-1}_{k=[\alpha(p+q)]}\{-\frac{qk}{p+q}\}-\sum\limits^{p+2q-1}_{[\alpha(p+2q)]}\{-\frac{qk}{p+2q}\}$.
Here $p,q$ are naturals, $0<\al …
- 2,232
2
votes
2
answers
401
views
On lower/upper bounds for Dedekind sum
The Dedekind sum $s(p,q)$ can be both positive and negative. What are the known lower/upper bounds in terms of p,q? (I would prefer something that grows not faster than q)
- 2,232
3
votes
2
answers
826
views
Counting integral points of a polytope in R^3 (the c_1 coefficient of Ehrhart polynomial)
(Sorry I'm outsider in this field.)
I need to count the number of integral points in a convex polytope in $\mathbf{R}^3$. The cones in the dual fan are not necessarily regular (does it create any pro …
- 2,232
2
votes
1
answer
300
views
the sum of fractional parts times the ordinary powers
Is there any way to compute/express $\sum\limits^m_{i=0}\{\frac{q*i}{m}\}(\frac{i}{m})^n$ ? Here $q,m,n$ are natural numbers, one can assume $gcd(q,m)=1$. Furthermore, $n$ can be treated as a parame …
- 2,232