7 citations · 44 across the 35 of their papers we have counts for
11 papers · 1 filter
Sums of Cusp Form Coefficients Along Quadratic Sequences
Chan Ieong Kuan, David Lowry-Duda, Alexander Walker +1
Let be a cusp form of weight on with character . By studying a certain shifted convolution sum, we prove that $\sum_{n \…
Small diameters and generators for arithmetic lattices in and certain Ramanujan graphs
Raphael S. Steiner
We show that arithmetic lattices in , stemming from the proper units of an Eichler order in an indefinite quaternion algebra over , admit a…
Theta functions, fourth moments of eigenforms, and the sup-norm problem II
Ilya Khayutin, Paul D. Nelson, Raphael S. Steiner
For an -normalized holomorphic newform of weight on a hyperbolic surface of volume attached to an Eichler order of squarefree level in an indefinite quaternion alg…
Theta functions, fourth moments of eigenforms, and the sup-norm problem I
Ilya Khayutin, Raphael S. Steiner
We give sharp point-wise bounds in the weight-aspect on fourth moments of modular forms on arithmetic hyperbolic surfaces associated to Eichler orders. Therefore we strengthen a re…
Sup-norm of Hecke-Laplace Eigenforms on
Raphael S. Steiner
We prove sub-convex bounds on the fourth moment of Hecke-Laplace eigenforms on . As a corollary, we get a bound on the sup-norm on an individual eigenform, which constitutes a…
On a Twisted Version of Linnik and Selberg's Conjecture on Sums of Kloosterman Sums
Raphael S. Steiner
We generalise the work of Sarnak-Tsimerman to twisted sums of Kloosterman sums and thus give evidence towards the twisted Linnik-Selberg Conjecture.
A conjectural extension of Hecke's converse theorem
Sandro Bettin, Jonathan W. Bober, Andrew R. Booker +6
We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main…
Near Counterexamples to Weil's Converse Theorem
Raphael S. Steiner
We show that in Weil's converse theorem the functional equations of multiplicative twists for at least the first moduli are needed in order to prove the mod…
Effective Vinogradov's mean value theorem via efficient boxing
Raphael S. Steiner
We combine Wooley's efficient congruencing method with earlier work of Vinogradov and Hua to get effective bounds on Vinogradov's mean value theorem.
Supnorm of Modular Forms of half-integral Weight in the Weight Aspect
Raphael S. Steiner
We bound the supnorm of half-integral weight Hecke eigenforms in the Kohnen plus space of level in the weight aspect, by combining bounds obtained from the Fourier expansion wi…
Uniform bounds on sup-norms of holomorphic forms of real weight
Raphael S. Steiner
We establish uniform bounds for the sup-norms of modular forms of arbitrary real weight with respect to a finite index subgroup of . We also prov…