Unitary Kloosterman Sums and the Gelfand–Graev Representation of GL2

heterogeneity within the orientalist discourse: representation of the orient in womens travelogues and mens paintings

from 1950s onward, new theories and critical approaches burgeoned across humanities. these theories were context-oriented; as a result, the analysis of discursive practices gained significance. thus, social, political, historical and cultural discourses that have been hitherto marginalized and considered inferior to literary texts, were introduced as important texts to be analyzed by critics. o...

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...

The Value 4 of Binary Kloosterman Sums

Kloosterman sums have recently become the focus of much research, most notably due to their applications in cryptography and their relations to coding theory. Very recently Mesnager has showed that the value 4 of binary Kloosterman sums gives rise to several infinite classes of bent functions, hyper-bent functions and semi-bent functions in even dimension. In this paper we analyze the different...