Skip to main content
MathOverflow

Return to Question

LaTeX the title and notation
Source Link
Peter Humphries
Peter Humphries
  • 8.4k
  • 3
  • 51
  • 75

Lower bound of first moment of $L$-function on $GL$\mathrm{GL}(3)$

Let $\pi$ be an automorphic form on $GL(3,\mathbb A_\mathbb Q)$$\mathrm{GL}(3,\mathbb{A}_{\mathbb{Q}})$. Do we know any case that $$\int_0^{T} \left|L(\frac 1 2 + it, \pi)\right| dt \gg T$$\[\int_0^{T} \left|L(\frac{1}{2} + it, \pi)\right| dt \gg T\] holds unconditionally?

I know the conjectured asymptotic formula is $T \log^* T$.

Lower bound of first moment of $L$-function on $GL(3)$

Let $\pi$ be an automorphic form on $GL(3,\mathbb A_\mathbb Q)$. Do we know any case that $$\int_0^{T} \left|L(\frac 1 2 + it, \pi)\right| dt \gg T$$ holds unconditionally?

I know the conjectured asymptotic formula is $T \log^* T$.

Lower bound of first moment of $L$-function on $\mathrm{GL}(3)$

Let $\pi$ be an automorphic form on $\mathrm{GL}(3,\mathbb{A}_{\mathbb{Q}})$. Do we know any case that \[\int_0^{T} \left|L(\frac{1}{2} + it, \pi)\right| dt \gg T\] holds unconditionally?

I know the conjectured asymptotic formula is $T \log^* T$.

LaTeX the title and notation
Source Link
edit approved Oct 20, 2014 at 5:03
Paul
edit approved Oct 20, 2014 at 5:03
Paul
  • 501
  • 1
  • 6
  • 18

Lower bound of 1stfirst moment of L$L$-function on GL$GL(3)$

Let $\pi$ be an automorphic form on GL$(3,\mathbb A_\mathbb Q)$$GL(3,\mathbb A_\mathbb Q)$. Do we know any case that $$\int_0^{T} \left|L(\frac 1 2 + it, \pi)\right| dt \gg T$$ holds unconditionally?

I know the conjectured asymptotic formula is $T \log^* T$.

Lower bound of 1st moment of L-function on GL(3)

Let $\pi$ be an automorphic form on GL$(3,\mathbb A_\mathbb Q)$. Do we know any case that $$\int_0^{T} \left|L(\frac 1 2 + it, \pi)\right| dt \gg T$$ holds unconditionally?

I know the conjectured asymptotic formula is $T \log^* T$.

Lower bound of first moment of $L$-function on $GL(3)$

Let $\pi$ be an automorphic form on $GL(3,\mathbb A_\mathbb Q)$. Do we know any case that $$\int_0^{T} \left|L(\frac 1 2 + it, \pi)\right| dt \gg T$$ holds unconditionally?

I know the conjectured asymptotic formula is $T \log^* T$.

Source Link
7-adic
7-adic
  • 3.8k
  • 24
  • 40

Lower bound of 1st moment of L-function on GL(3)

Let $\pi$ be an automorphic form on GL$(3,\mathbb A_\mathbb Q)$. Do we know any case that $$\int_0^{T} \left|L(\frac 1 2 + it, \pi)\right| dt \gg T$$ holds unconditionally?

I know the conjectured asymptotic formula is $T \log^* T$.