By Yoichi Motohashi

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Additional info for Analytic Number Theory

Sample text

Now note that if V is admissible, then the sequence v 4- 1, v G V, is also admissible; this follows from (1) and (2). Goldbach Numbers and Uniform Distribution 49 Hence, (16) also holds with [v] + 1 in place of [v]. Therefore, the number of v X(logX)-B/8.

C. Vaughan. The exceptional set in Goldbach's problem. , 27 (1975), 353-370. [5] A. Perelli. Goldbach numbers represented by polynomials. Rev. Mat. Iberoamericana, 12 (1996), 477-490. C. Vaughan. The Hardy-Littlewood Method. Cambridge Univ. Press, London, 1981. Jorg Briidern Mathematisches Institut A, Universitat Stuttgart Pfaffenwaldring 57, D-70550 Stuttgart, Germany Alberto Perelli Dipartimento di Matematica, Universita di Genova Via Dodecaneso 35, 1-16146, Genova, Italy The Number of Algebraic Numbers of Given Degree Approximating a Given Algebraic Number JAN-HENDRIK EVERTSE 1.

D. (II) We shall also suppose that P 0. (Ill) Each Lj is assumed to have an analytic continuation to all of C as a meromorphic function of finite order with a finite number of poles, all on the line a = 1, and to satisfy a functional equation of the form f With respect to [1], we do not ask here that the Lj satisfy the same functional equation in (///). 32 E. Bombieri and A. Perelli where \$j(s) = Qj II™ 1 r (Ai? , L^ will be assumed to satisfy for X > 2, certain positive constants n i , .