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Results tagged with nt.number-theory
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user 38104
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
0
votes
Estimates on derivatives of Bessel function
you can see http://arxiv.org/abs/1408.5652v1 for some reference
- 177
4
votes
On the prime number theorem in arithmetic progression
Siegel - Walfisz theorem states
$$\psi(x,q;a)=x/\phi(q)+O(x/\log^Ax)$$when q is small;q is big ,the results is trival . (When is the Siegel-Walfisz theorem non-trivial?)
if $q \ll log^Ax$,we have
$ …
- 177
4
votes
Lower bound of first moment of $L$-function on $\mathrm{GL}(3)$
see http://www.ams.org/journals/proc/2009-137-11/S0002-9939-09-10012-6/S0002-9939-09-10012-6.pdf ,where the low bound $T$ was obtained unconditionally for any $G_m(\mathbb{Q_A})$ and any power of pos …
- 177
1
vote
1
answer
270
views
Does $L(-1+it,f)\ll_f \log^c q(f)t$ hold ture?
Let $f$ be a holomorphic or Maass cusp form for $SL(2,Z)$. Define $L(s,f)=\sum_{n\ge 1}\frac{a_f(n)}{n^s}$, for $\Im s$ sufficiently large.
Then
$$L(-1+it,f)\ll_f \log^c q(f)t$$
holds, for some conat …
- 177
0
votes
Asymptotic formula for the number of ways to write a number as the sum of $k$ triangular num...
Use circle method detect the condition $N=\sum_{i=1}^k \frac{m_i(m_i+1)}{2}$ to derive
$r(N)=\int_0^1 f^k(\alpha) e(-N\alpha)$, where $f(\alpha)=\sum_{n\leq N} e(\alpha \frac{m_i(m_i+1)}{2} )=\int_ …
6
votes
1
answer
1k
views
subconvexity problem for $GL(3) × GL(2)$ $L$-function without involving in symmetric lift
A question in study of subconvexity topic puzzles me for a long time, which mabe a stupid question for many experts. I really wish someone to help me out, and any advice will be highly appreciated.
L …
- 177
1
vote
1
answer
736
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stationary phase method in analytic number theory
I hope someone can tell me something about the error term in the formula calculating the oscillatory integral like $\int_a^b g(x)e(f(x))d x$. Specially, the exact formula on page 114 of M. Huxley's gr …
- 177