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Finding Significant Fourier Coefficients: Clarifications, Simplifications, Applications and Limitations
Significant Fourier transform Goldreich-Levin algorithm Kushilevitz-Mansour algorithm
2016/7/13
Ideas from Fourier analysis have been used in cryptography for three decades. Akavia, Goldwasser
and Safra unified some of these ideas to give a complete algorithm that finds significant
Fourier coe...
POWER RESIDUES OF FOURIER COEFFICIENTS OF ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION
Elliptic curve a prime number parathyroid hormone Fourier coefficient
2014/12/24
Fix m greater than one and let E be an elliptic curve over Q with complex multiplication. We formulate conjectures on the density of primes p (congruent to one modulo m) for which the pth Fourier coef...
Fourier coefficients of noncongruence cuspforms
Fourier coefficients noncongruence cuspforms
2011/1/21
Given a finite index subgroup of SL2(Z) with modular curve defined over Q,under the assumption that the space of weight k (≥ 2) cusp forms is 1-dimensional, we show that a form in this space with Four...
On the Fourier coefficients of 2-dimensional vector-valued modular forms
Fourier coefficients 2-dimensional vector-valued modular forms
2010/11/30
Let : SL(2,Z) → GL(2,C) be an irreducible representation of the modular group such that (T) has finite order N. We study holomorphic vector-valued modular forms F( ) of integral weight associated ...
A Note on the Magnitude of Walsh Fourier Coefficients
Functions of $p-$bounded variation $phi-$bounded variation $p-Lambda-$bounded variation and of $phi-Lambda-$bounded variation Walsh Fourier coefficients Integral modulus continuity of order $p$
2010/1/25
In this note, the order of magnitude of Walsh Fourier coefficients for functions of the classes , , and is studied. For the classes and Taibleson-like technique for Walsh Fourier coefficien...
Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms
representation of numbers quadratic forms generalized theta series Fourier coefficient of cusp forms
2010/2/26
In this paper, representations of positive integers by certain quadratic forms Qp defined for odd prime p are examined. The number of representations of positive integer n by the quadratic form Qp, is...
On the Asymptotics of Fourier Coefficients for the Potential in Hill's Equation
Fourier Coefficients Hill's Equation
2010/3/1
We consider Hill's equation y'' +(l -q)y=0 where q\in L1[0,p ]. We show that if ln-the length of the n-th instability interval- is of order O(n-k) then the real Fourier coefficients an,bn of q are of ...