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On the almost Goldbach problem of Linnik

Jianya Liu, Ming-Chit Liu, Tianze Wang (1999)

Journal de théorie des nombres de Bordeaux

Under the Generalized Riemann Hypothesis, it is proved that for any k 200 there is N k > 0 depending on k only such that every even integer N k is a sum of two odd primes and k powers of 2 .

On the annihilating ideal for trace forms

Martin Epkenhans (2003)

Journal de théorie des nombres de Bordeaux

We give several examples of classes of trace forms for which the ideal of annihilating polynomials is principal. We prove, that in general, the annihilating ideal is not a principal ideal.

On the apostol-bernoulli polynomials

Qiu-Ming Luo (2004)

Open Mathematics

In the present paper, we obtain two new formulas of the Apostol-Bernoulli polynomials (see On the Lerch Zeta function. Pacific J. Math., 1 (1951), 161–167.), using the Gaussian hypergeometric functions and Hurwitz Zeta functions respectively, and give certain special cases and applications.

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