Browsing by Author "Inam, Ilker"

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On the Distribution of Coefficients of Half-Integral Weight Modular Forms and the Bruinier-Kohnen Conjecture
(Tubitak Scientific & Technological Research Council Turkey, 2021) Inam, Ilker; Demirkol Ozkaya, Zeynep; Tercan, Elif; Wiese, Gabor
This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level Gamma 0(4) and half-integral weights. Based on substantial calculations, the question is raised whether the distribution of normalised Fourier coefficients with bounded indices can be approximated by a generalised Gaussian distribution. Moreover, it is argued that the apparent symmetry around zero of the data lends strong evidence to the Bruinier-Kohnen conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently.
On Tribonacci Numbers Written as a Product of Two Perrin Numbers
(World Scientific Publ Co Pte Ltd, 2025) Demirkol Ozkaya, Zeynep; Inam, Ilker; Senadim, Meltem
In this paper, we give all solutions of the Diophantine equation T-n = RkRm, where (n,k,m) is an element of Z(+) x Z(+) x Z(+), Rk is the Perrin sequence, and T-n is the Tribonacci sequence. We show that this Diophantine equation has only 7 integer solution triples. For the proof, we use Baker's method. Our motivation is to show that linear forms in logarithms can still be effectively used for the solutions of different Diophantine equations involving classical number sequences such as Fibonacci or Lucas sequences.