61 citations · 272 across the 16 of their papers we have counts for
16 papers
The cubic moment of -functions for specified local component families
Yueke Hu, Ian Petrow, Matthew P. Young
We prove Lindelöf-on-average upper bounds on the cubic moment of central values of -functions over certain families of automorphic representati…
A generalized PGL(2) Petersson/Bruggeman-Kuznetsov formula for analytic applications
Yueke Hu, Ian Petrow, Matthew P. Young
We develop generalized Petersson/Bruggeman-Kuznetsov (PBK) formulas for specified local components at non-archimedean places. In fact, we introduce two hypotheses on non-archimedea…
The volumes of Miyauchi subgroups
Didier Lesesvre, Ian Petrow
Miyauchi described the and -factors attached to generic representations of the unramified unitary group of rank three in terms of local newforms defined by a seque…
The fourth moment of Dirichlet -functions along a coset and the Weyl bound
Ian Petrow, Matthew P. Young
We prove a Lindelöf-on-average upper bound for the fourth moment of Dirichlet -functions of conductor along a coset of the subgroup of characters modulo when , wh…
The Weyl bound for Dirichlet -functions of cube-free conductor
Ian Petrow, Matthew P. Young
We prove a Weyl-exponent subconvex bound for any Dirichlet -function of cube-free conductor. We also show a bound of the same strength for certain -functions of self-dual $\m…
The Weyl law for algebraic tori
Ian Petrow
We give an asymptotic evaluation for the number of automorphic characters of an algebraic torus with bounded analytic conductor. The analytic conductor which we use is defined…
Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field
Ian Petrow
We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to certain congruence subgroups. Such an estimate has applicatio…
Oscillatory integrals with uniformity in parameters
Eren Mehmet Kiral, Ian Petrow, Matthew P. Young
We prove a sharp asymptotic formula for certain oscillatory integrals that may be approached using the stationary phase method. The estimates are uniform in terms of auxiliary para…
A generalized cubic moment and the Petersson formula for newforms
Ian Petrow, Matthew P. Young
Using a cubic moment, we prove a Weyl-type subconvexity bound for the quadratic twists of a holomorphic newform of square-free level, trivial nebentypus, and arbitrary even weight.…
Counting Automorphic Forms on Norm One Tori
Ernest Hunter Brooks, Ian Petrow
We give an asymptotic formula for the number of automorphic forms on the non-split norm one torus associated with an imaginary quadratic extension of , ordered by a…
Elliptic curves over a finite field and the trace formula
Nathan Kaplan, Ian Petrow
We prove formulas for power moments for point counts of elliptic curves over a finite field such that the groups of -points of the curves contain a chosen subgroup. These fo…
Traces of Hecke Operators and Refined Weight Enumerators of Reed-Solomon Codes
Nathan Kaplan, Ian Petrow
We study the quadratic residue weight enumerators of the dual projective Reed-Solomon codes of dimensions and over the finite field . Our main results are f…
A Twisted Motohashi Formula and Weyl-Subconvexity for -functions of Weight Two Cusp Forms
Ian Petrow
We derive a Motohashi-type formula for the cubic moment of central values of -functions of level cusp forms twisted by quadratic characters of conductor , previously stud…
A Recursion Formula for Moments of Derivatives of Random Matrix Polynomials
S. Ali Altug, Sandro Bettin, Ian Petrow +2
We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N) and O^-(2N). These averages are used to predict…
Moments of L'(1/2) in the Family of Quadratic Twists
Ian Petrow
We prove the asymptotic formulae for several moments of derivatives of GL(2) L-functions over quadratic twists. The family of L-functions we consider has root number fixed to -1 an…
Transition Mean Values of Shifted Convolution Sums
Ian Petrow
Let f be a classical holomorphic cusp form for SL_2(Z) of weight k which is a normalized eigenfunction for the Hecke algebra, and let λ(n) be its eigenvalues. In this paper we stud…