Publication
Computing Roots of Polynomials over Function Fields of Curves
Publications associées (66)
On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros
Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, an ...
MDPI2024Finite free convolutions of polynomials
We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric addi ...
SPRINGER HEIDELBERG2022Singularities of general fibers and the LMMP
Zsolt Patakfalvi, Joseph Allen Waldron
We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by p - 1. We deduce ...
JOHNS HOPKINS UNIV PRESS2022A PCP Theorem for Interactive Proofs and Applications
The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads O(1) bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multi ...
SPRINGER INTERNATIONAL PUBLISHING AG2022Interlacing families III: Sharper restricted invertibility estimates
We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri's Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by the Schatten 4-norm ...
HEBREW UNIV MAGNES PRESS2021Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths
In this paper we study the moments of polynomials from the Askey scheme, and we focus on Askey-Wilson polynomials. More precisely, we give a combinatorial proof for the case where d = 0. Their values have already been computed by Kim and Stanton in 2015, h ...
ELECTRONIC JOURNAL OF COMBINATORICS2021Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing
Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...
CAMBRIDGE UNIV PRESS2021Resonance Frequency Dependence Of A1 Lamb Mode On The Pitch Of The Electrode Structure
Luis Guillermo Villanueva Torrijo, Seniz Esra Küçük, Soumya Yandrapalli, Victor Plessky
Dispersion of A1 Lamb mode near onset frequency is discussed. This mode is close to that used in XBAR devices. The typically used approximation is based on elliptic form of slowness curve and ignoring mode interaction is not valid for widely used materials ...
IEEE2021Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications
We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...
2020Single and multiple recurrence along non-polynomial sequences
We establish new recurrence and multiple recurrence results for a rather large family of non-polynomial functions which contains tempered functions and (non-polynomial) functions from a Hardy field with polynomial growth. In particular, we show that, somew ...
2020