Yazar "Yalciner, Aynur" seçeneğine göre listele

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    Arithmetic properties of coefficients of L-functions of elliptic curves
    (SPRINGER WIEN, 2018) Guloglu, Ahmet M.; Luca, Florian; Yalciner, Aynur
    Let n = 1 ann -s be the L-series of an elliptic curve E defined over the rationals without complex multiplication. In this paper, we present certain similarities between the arithmetic properties of the coefficients {an}8 n= 1 and Euler's totient function.(n). Furthermore, we prove that both the set of n such that the regular polygon with | an| sides is ruler-and-compass constructible, and the set of n such that n-an + 1 =.(n) have asymptotic density zero. Finally, we improve a bound of Luca and Shparlinski on the counting function of elliptic pseudoprimes.
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    L-FUNCTIONS OF ELLIPTIC CURVES AND BINARY RECURRENCES
    (CAMBRIDGE UNIV PRESS, 2013) Luca, Florian; Oyono, Roger; Yalciner, Aynur
    Let L(s; E) = Sigma(n >= 1)a(n)n(-s) be the L-series corresponding to an elliptic curve E defined over Q and u = {u(m)}(m >= 0) be a nondegenerate binary recurrence sequence. We prove that if M-E is the set of n such that a(n) not equal 0 and N-E is the subset of n is an element of M-E such that vertical bar a(n)vertical bar = vertical bar u(m)vertical bar holds with some integer m >= 0, then N-E is of density 0 as a subset of M-E.
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    A Matrix Approach for Divisibility Properties of the Generalized Fibonacci Sequence
    (HINDAWI PUBLISHING CORPORATION, 2013) Yalciner, Aynur
    We give divisibility properties of the generalized Fibonacci sequence by matrix methods. We also present new recursive identities for the generalized Fibonacci and Lucas sequences.
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    NEW SUMS IDENTITIES IN WEIGHTED CATALAN TRIANGLE WITH THE POWERS OF GENERALIZED FIBONACCI AND LUCAS NUMBERS
    (CHARLES BABBAGE RES CTR, 2014) Kilic, Emrah; Yalciner, Aynur
    In this paper, we consider a generalized Catalan triangle defined by k(m)/n(2n n - k) for positive integer m. Then we compute the weighted half binomial sums with the certain powers of generalized Fibonacci and Lucas numbers of the form Sigma(n)(k=0) (2n n + k) k(m)/nX(tk)(r), where X-n either generalized Fibonacci or Lucas numbers, t and r are integers for 1 <= m <= 6. After we describe a general methodology to show how to compute the sums for further values of m.
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    ON GENERALIZATIONS OF TWO CURIOUS DIVISIBILITY PROPERTIES
    (UNIV MISKOLC INST MATH, 2013) Yalciner, Aynur
    In this paper, we extend two curious divisibility properties for the general second order linear recurrence {U-n(p, q)}. We also give new recursive identities for the general second linear recurrences {U-n(p, q)} and {V-n(p, q)}. These results generalize the results given by E. Kilic, "A matrix approach for generalizing two curious divisibility properties", Miskolc Math. Notes, vol. 13., No. 2, pp. 389-396, 2012.
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    On sums of squares of Fibonomial coefficients by q-calculus
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2016) Kilic, Emrah; Yalciner, Aynur
    We present some new kinds of sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. As proof method, we will follow the method given in [E. Kili, c and H. Prodinger, Closed form evaluation of sums containing squares of Fibonomial coefficients, accepted in Math. Slovaca]. For this, first we translate everything into q-notation, and then to use generating functions and Rothe's identity from classical q-calculus.
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    SOME NEW FINITE SUMS INVOLVING GENERALIZED FIBONACCI AND LUCAS NUMBERS
    (CHARLES BABBAGE RES CTR, 2016) Yalciner, Aynur
    In this paper, we compute various finite sums that alternate according to (-1)((kn)) involving the generalized Fibonacci and Lucas numbers for k = 3, 4, 5 and even k of the form 2(m) with m > 1.
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    Squares in a certain sequence related to L-functions of elliptic curves
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2013) Luca, Florian; Yalciner, Aynur
    Let L(s, E) = Sigma(n >= 1) a(n)n(-s) be the L-series corresponding to an elliptic curve E defined over Q and satisfying certain technical conditions. We prove that the set of positive integers n such that n(2) - a(n2) + 1 = square has asymptotic density 0. (C) 2013 Elsevier Inc. All rights reserved.