19 citations · 76 across the 12 of their papers we have counts for
19 papers
Bessel Functions on GL(n), II -- The case
Jack Buttcane
The purpose of this article is to verify the conjectures of the previous paper in the particular case of . We accomplish this in general, but observe two failures of the con…
Bessel functions on GL(n), I
Jack Buttcane
In the context of the Kuznetsov trace formula, we outline the theory of the Bessel functions on as a series of conjectures designed as a blueprint for the construction of K…
On Sums of hyper-Kloosterman Sums
Jack Buttcane
A formula of Kuznetsov allows one to interpret a smooth sum of Kloosterman sums as a sum over the spectrum of automorphic forms. In this paper, we construct a similar formu…
The arithmetic Kuznetsov formula on , II: The general case
Jack Buttcane
We obtain the last of the standard Kuznetsov formulas for . In the previous paper, we were able to exploit the relationship between the positive-sign Bessel function…
Subconvexity for L-functions of non-spherical cusp forms on GL(3)
Valentin Blomer, Jack Buttcane
Let f be a cusp form for SL(3, Z) associated with a generalized principal series representation of minimal weight d, spectral parameter r and associated L-function L(s, f). For $r…
The arithmetic Kuznetsov formula on , I: The Whittaker case
Jack Buttcane
The original formulae of Kuznetsov for allowed one to study either a spectral average via Kloosterman sums or to study an average of Kloosterman sums via a spect…
Kuznetsov, Petersson and Weyl on , II: The generalized principal series forms
Jack Buttcane
This paper initiates the study by analytic methods of the generalized principal series Maass forms on . These forms occur as an infinite sequence of one-parameter families i…
Kuznetsov, Petersson and Weyl on GL(3), I: The principal series forms
Jack Buttcane
The Kuznetsov and Petersson trace formulae for forms may collectively be derived from Poincaré series in the space of Maass forms with weight. Having already developed the…
Weights, raising and lowering operators, and K-types for automorphic forms on SL(3,R)
Jack Buttcane, Stephen D. Miller
We give a fully explicit description of Lie algebra derivatives (generalizing raising and lowering operators) for representations of SL(3,R) in terms of a basis of Wigner functions…
Higher Weight on GL(3), II - The cusp forms
Jack Buttcane
The purpose of this paper is to collect and make explicit the results of Gel'fand, Graev and Piatetski-Shapiro and Miyazaki for the cusp forms which are non-trivial on $SO(…
Plancherel distribution of Satake parameters of Maass cusp forms on
Jack Buttcane, Fan Zhou
We prove an equidistribution result for the Satake parameters of Maass cusp forms on with respect to the -adic Plancherel measure by using an application of the Kuznetsov…
On the fourth moment of Hecke Maass forms and the Random Wave Conjecture
Jack Buttcane, Rizwanur Khan
Conditionally on the Generalized Lindelöf Hypothesis, we obtain an asymptotic for the fourth moment of Hecke Maass cusp forms of large Laplacian eigenvalue for the full modular gro…
Higher weight on GL(3), I: The Eisenstein series
Jack Buttcane
The purpose of this paper is to collect and make explicit the results of Langlands, Bump, Miyazaki and Manabe, Ishii and Oda for the Eisenstein series and Whittaker functio…
Global decomposition of GL(3) Kloosterman sums and the spectral large sieve
Valentin Blomer, Jack Buttcane
We prove best-possible bounds for bilinear forms in Kloosterman sums for GL(3) associated with the long Weyl element. As an application we derive a best-possible spectral large sie…
On the subconvexity problem for L-functions on GL(3)
Valentin Blomer, Jack Buttcane
Let f be a cusp form for the group SL(3, Z) with Langlands parameter mu and associated L-function L(s, f). If mu is in generic position, i.e. away from the Weyl chamber walls and a…
The Spectral Kuznetsov Formula on SL(3)
Jack Buttcane
The Kuznetsov formula exists in several versions, and has been employed with some success to study automorphic forms on . In each version, the weight functions on th…
A mean value of a triple product of -functions
Jack Buttcane, Rizwanur Khan
Luo has proven an optimal upper bound for the -norm of dihedral Maass forms of large eigenvalue, by bounding a mean value of triple product -functions. Motivated by this re…
-norms of Hecke newforms of large level
Jack Buttcane, Rizwanur Khan
We prove a new upper bound for the -norm of a holomorphic Hecke newform of large fixed weight and prime level . This is achieved by proving a sharp mean value est…
On Sums of SL(3,Z) Kloosterman Sums
Jack Buttcane
We show that sums of the SL(3,Z) long element Kloosterman sum against a smooth weight function have cancellation due to the variation in argument of the Kloosterman sums, when each…