Analogues of Newton-Girard power-sum formulas for entire and meromorphic functions with applications to the Riemann zeta function

作者：Bagdasaryan Armen; Araci Serkan^*; Acikgoz Mehmet; Srivastava H M

来源：Journal of Number Theory, 2015, 147: 92-102.

DOI：10.1016/j.jnt.2014.07.006

• Meromorphic functions
• Entire functions
• Functions of finite order
• Zeros and poles
• Sums of reciprocal powers of zeros and poles
• Riemann zeta function
• Nontrivial zeros of zeta function
• Sums of powers of zeros of the
• Riemann zeta function
• Gamma function
• Recurrence relations

The Newton power-sum formulas relate to sums of powers of roots of a polynomial with the coefficients of the polynomial. In this paper we obtain formulas that relate to sums of reciprocal powers of zeros and poles of entire and meromorphic functions with the coefficients of their Taylor series expansions. We then derive the recurrence formulas for the Riemann zeta function at integer arguments and compute the sums extended over the nontrivial zeros of the Riemann zeta function.

• 出版日期2015-2