42 citations · 108 across the 12 of their papers we have counts for
15 papers
Log-Normal Multiplicative Dynamics for Stable Low-Precision Training of Large Networks
Keigo Nishida, Eren Mehmet Kıral, Kenichi Bannai +2
Studies in neuroscience have shown that biological synapses follow a log-normal distribution whose transitioning can be explained by noisy multiplicative dynamics. Biological netwo…
Guided Data Generation for Understanding Model Behavior
Eren Mehmet Kıral, Nurşen Aydın, Ş. İlker Birbil
We propose a method for generating distributions over the input space as an inspection tool for understanding trained models. Our framework poses questions of the form ``which inpu…
The Lie-Group Bayesian Learning Rule
Eren Mehmet Kıral, Thomas Möllenhoff, Mohammad Emtiyaz Khan
The Bayesian Learning Rule provides a framework for generic algorithm design but can be difficult to use for three reasons. First, it requires a specific parameterization of expone…
Subconvexity for twisted GL(3) L-functions
Eren Mehmet Kıral, Chan Ieong Kuan, Didier Lesesvre
Using the circle method, we obtain subconvex bounds for GL(3) L-functions twisted by a character modulo a prime p, hybrid in the t and p-aspects.
Parametrization of Kloosterman sets and -Kloosterman sums
Eren Mehmet Kıral, Maki Nakasuji
We stratify the big cell Kloosterman sets using the reduced word decomposition of the Weyl group element, inspired by the Bott-Samelson factorization. Thus the $\ma…
Level Reciprocity in the twisted second moment of Rankin-Selberg L-functions
Nickolas Andersen, Eren Mehmet Kiral
We prove an exact formula for the second moment of Rankin-Selberg -functions twisted by , where is a fixed holomorphic cusp form and is summe…
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.
The Voronoi formula and double Dirichlet series
Eren Mehmet Kiral, Fan Zhou
We prove a Voronoi formula for coefficients of a large class of -functions including Maass cusp forms, Rankin-Selberg convolutions, and certain isobaric sums. Our proof is based…
Opposite Sign Kloosterman Sum Zeta Function
Eren Mehmet Kiral
We study the meromorphic continuation and the spectral expansion of the oppposite sign Kloosterman sum zeta function, $$(2π\sqrt{mn})^{2s-1}\sum_{\ell=1}^\infty \frac{S(m,-n,\ell)}…
Bounds on sup-norms of half-integral weight modular forms
Eren Mehmet Kiral
Bounding sup-norms of modular forms in terms of the level has been the focus of much recent study. In this work the sup norm of a half integral weight cusp form is bounded in terms…
Counting Square Discriminants
Thomas A. Hulse, E. Mehmet Kıral, Chan Ieong Kuan +1
Counting integral binary quadratic forms with certain restrictions is a classical problem. In this paper, we count binary quadratic forms of fixed discriminant given restrictions o…
Subconvexity for Half Integral Weight -functions
Eren Mehmet Kiral
We prove a subconvexity bound in the conductor aspect for where is a half integer weight modular form. This -function has analytic continuation and functional equ…
The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms
Thomas A. Hulse, E. Mehmet Kiral, Chan Ieong Kuan +1
From a result of Waldspurger, it is known that the normalized Fourier coefficients of a half-integral weight holomorphic cusp eigenform $\f$ are, up to a finite set of facto…