150 citations · 1.1k across the 47 of their papers we have counts for
47 papers
Vanishing of Quartic and Sextic Twists of -functions
Jennifer Berg, Nathan C. Ryan, Matthew P. Young
Let be an elliptic curve over . We conjecture asymptotic estimates for the number of vanishings of as varies over all primitive Dirichlet characters…
The large sieve for self-dual Eisenstein series of varying levels
Matthew P Young
We prove an essentially optimal large sieve inequality for self-dual Eisenstein series of varying levels. This bound can alternatively be interpreted as a large sieve inequality fo…
Reciprocity and the Kernel of Dedekind Sums
Alexis LaBelle, Emily Van Bergeyk, Matthew P. Young
We use the action of Atkin-Lehner operators to generate a family of reciprocity formulas for newform Dedekind sums. This family of reciprocity formulas provides symmetries which we…
An improved spectral large sieve inequality for
Matthew P. Young
We prove an improved spectral large sieve inequality for the family of Hecke-Maass cusp forms. The method of proof uses duality and its structure reveals unexpec…
Moments and hybrid subconvexity for symmetric-square L-functions
Rizwanur Khan, Matthew P. Young
We establish sharp bounds for the second moment of symmetric-square -functions attached to Hecke Maass cusp forms with spectral parameter , where the second moment is…
The kernel of newform Dedekind sums
Evuilynn Nguyen, Juan J. Ramirez, Matthew P. Young
Newform Dedekind sums are a class of crossed homomorphisms that arise from newform Eisenstein series. We initiate a study of the kernel of these newform Dedekind sums. Our results…
Quantum Unique Ergodicity for Eisenstein Series in the Level Aspect
Jiakun Pan, Matthew P. Young
We prove a variety of quantum unique ergodicity results for Eisenstein series in the level aspect. A new feature of this variant of QUE is that the main term involves the logarithm…
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…
Dedekind sums arising from newform Eisenstein series
Tristie Stucker, Amy Vennos, Matthew P. Young
For primitive non-trivial Dirichlet characters and , we study the weight zero newform Eisenstein series at . The holomorphic part of this functio…
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…
Explicit calculations with Eisenstein series
Matthew P Young
We find explicit change-of-basis formulas between Eisenstein series attached to cusps, and newform Eisenstein series attached to pairs of primitive Dirichlet characters. As a conse…
Equidistribution of Eisenstein series on geodesic segments
Matthew P Young
We show an asymptotic formula for the L^2 norm of the Eisenstein series restricted to a segment of a geodesic connecting infinity and an arbitrary real. For generic geodesics of th…
Kloosterman sums and Fourier coefficients of Eisenstein series
Eren Mehmet Kiral, Matthew P. Young
We derive explicit formulas for some Kloosterman sums on , and for the Fourier coefficients of Eisenstein series attached to arbitrary cusps, around a general Atkin-Lehner…
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…
The Fifth Moment of modular L-functions
Eren Mehmet Kiral, Matthew P. Young
We prove a sharp bound on the fifth moment of modular L-functions of fixed small weight, and large prime level.
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.…
Sign changes of the Eisenstein series on the critical line
Junehyuk Jung, Matthew P. Young
We prove a quantitative lower bound on the number of nodal domains of the real-analytic Eisenstein series. The main tool in the proof is a quantitative restricted QUE theorem where…
Zeros of certain combinations of Eisenstein series
Sarah Reitzes, Polina Vulakh, Matthew P. Young
We prove that if and are sufficiently large, then all the zeros of the weight cusp form in the standard fundamental domain…
The restriction of the Eisenstein series to a geodesic segment
Matthew P. Young
We study the norm of the Eisenstein series restricted to a segment of a geodesic connecting infinity and an arbitrary real. We conjecture that on slightly thick…
Bilinear forms with Kloosterman sums and the spectral large sieve
Matthew P. Young
We analyze certain bilinear forms involving Kloosterman sums. As an application, we obtain an improved estimate for the spectral large sieve inequality.
A note on the sup norm of Eisenstein series
Matthew P. Young
We prove a sup norm bound on the real-analytic Eisenstein series, of the form , uniformly for in a fixed compact subset of $\mathbb{H}…
The number of solutions to Mordell's equations in constrained ranges
Matthew P. Young
We estimate the number of solutions to with , in terms of both and .
Weyl-type hybrid subconvexity bounds for twisted -functions and Heegner points on shrinking sets
Matthew P. Young
We prove a Weyl-type subconvexity bound for the central value of the -function of a Hecke-Maass form or a holomorphic Hecke eigenform twisted by a quadratic Dirichlet character,…
Zeros of the weight two Eisenstein Series
Rachael Wood, Matthew P. Young
We develop some of the finer details of the location of the zeros of the weight two Eisenstein series. These zeros are the same as the zeros of the derivative of the Ramanujan delt…