Global decomposition of GL(3) Kloosterman sums and the spectral large sieve

Bilinear Forms with Gl 3 Kloosterman Sums and the Spectral Large Sieve

We analyze certain bilinear forms involving GL3 Kloosterman sums. As an application, we obtain an improved estimate for the GL3 spectral large sieve inequality.

The spectral decomposition of shifted convolution sums

Let π1, π2 be cuspidal automorphic representations of PGL2(R) of conductor 1 and Hecke eigenvalues λπ1,2 (n), and let h > 0 be an integer. For any smooth compactly supported weight functions W1,2 : R → C and any Y > 0 a spectral decomposition of the shifted convolution sum

Legendre Sums, Soto-andrade Sums and Kloosterman Sums

The three sums named in the title are all known to appear in connection with the complex representation theory of GL(2, q). The first two are incarnations of certain spherical vectors, whereas the third is a matrix coefficient for a parabolic basis. In this work, Legendre and Soto-Andrade sums are shown to occur in a second way, as parabolic ClebschGordan coefficients for the tensor product of ...

On zeros of Kloosterman sums

On the Distribution of Kloosterman Sums

For a prime p, we consider Kloosterman sums Kp(a) = ∑ x∈F p exp(2πi(x + ax)/p), a ∈ Fp, over a finite field of p elements. It is well known that due to results of Deligne, Katz and Sarnak, the distribution of the sums Kp(a) when a runs through Fp is in accordance with the Sato–Tate conjecture. Here we show that the same holds where a runs through the sums a = u+v for u ∈ U , v ∈ V for any two s...