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Let {F n}n≥0 be the sequence of Fibonacci numbers. The aim of this paper is to give linear independence results over (5) for the infinite series n=1χj(n)/Fn with certain nonprincipal real Dirichlet characters χ j. We also deduce the irrationality results for the special principal Dirichlet characters and for other multiplicative functions.

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Abstract

For integers m, n, q, k, with q,k≧1 and Dirichlet characters we define a generalized Kloosterman sum

ea
with a Dirichlet character and a Gauss sum G(a,χ′) as coefficient, where e(z)=e 2πiz. The aim of this paper is to study the fourth power mean
eb
obtaining explicit formulas for M k(q).

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Abstract  

By using p-adic q-deformed fermionic integral on ℤp, we construct new generating functions of the twisted (h, q)-Euler numbers and polynomials attached to a Dirichlet character χ. By applying Mellin transformation and derivative operator to these functions, we define twisted (h, q)-extension of zeta functions and l-functions, which interpolate the twisted (h, q)-extension of Euler numbers at negative integers. Moreover, we construct the partially twisted (h, q)-zeta function. We give some relations between the partially twisted (h, q)-zeta function and twisted (h, q)-extension of Euler numbers.

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1993 5 411 484 Rakhmonov, Z. Kh. , On the distribution of values of Dirichlet characters and their

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