Skip to main content
MathOverflow

Return to Answer

replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
Source Link
Community Bot
Community Bot
  • 1
  • 2
  • 3

The partial sums, normalized by $\sqrt{p}$, are unbounded, as one varies $a$ over all invertible classes modulo $p$n and lets $p$ go to infinity. This follows from results in this paperthis paper, which also has more precise information on the distribution of the partial sums, including real and imaginary parts.

(By the way, it is more usual to write $ax+x^{-1}$ in the phase of the Kloosterman sum, instead of $x+ax^{-1}$; this emphasizes that it is, as a function of $a$, the discrete Fourier transform of $e_p(x^{-1})$).

The partial sums, normalized by $\sqrt{p}$, are unbounded, as one varies $a$ over all invertible classes modulo $p$n and lets $p$ go to infinity. This follows from results in this paper, which also has more precise information on the distribution of the partial sums, including real and imaginary parts.

(By the way, it is more usual to write $ax+x^{-1}$ in the phase of the Kloosterman sum, instead of $x+ax^{-1}$; this emphasizes that it is, as a function of $a$, the discrete Fourier transform of $e_p(x^{-1})$).

The partial sums, normalized by $\sqrt{p}$, are unbounded, as one varies $a$ over all invertible classes modulo $p$n and lets $p$ go to infinity. This follows from results in this paper, which also has more precise information on the distribution of the partial sums, including real and imaginary parts.

(By the way, it is more usual to write $ax+x^{-1}$ in the phase of the Kloosterman sum, instead of $x+ax^{-1}$; this emphasizes that it is, as a function of $a$, the discrete Fourier transform of $e_p(x^{-1})$).

Source Link
Denis Chaperon de Lauzières
Denis Chaperon de Lauzières
  • 396
  • 2
  • 3

The partial sums, normalized by $\sqrt{p}$, are unbounded, as one varies $a$ over all invertible classes modulo $p$n and lets $p$ go to infinity. This follows from results in this paper, which also has more precise information on the distribution of the partial sums, including real and imaginary parts.

(By the way, it is more usual to write $ax+x^{-1}$ in the phase of the Kloosterman sum, instead of $x+ax^{-1}$; this emphasizes that it is, as a function of $a$, the discrete Fourier transform of $e_p(x^{-1})$).