Details

Autor(en) / Beteiligte

• Mora, G.
• Benítez, E.

Titel

Essential bounds of Dirichlet polynomials

Ist Teil von

• Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2021-07, Vol.115 (3), Article 107

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2021

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper we have given conditions on exponential polynomials P n ( s ) of Dirichlet type to be attained the equality between each of two pairs of bounds, called essential bounds, a P n ( s ) , ρ N and b P n ( s ) , ρ 0 associated with P n ( s ) . The reciprocal question has been also treated. The bounds a P n ( s ) , b P n ( s ) are defined as the end-points of the minimal closed and bounded real interval I = [ a P n ( s ) , b P n ( s ) ] such that all the zeros of P n ( s ) are contained in the strip I × R of the complex plane C . The bounds ρ N , ρ 0 are defined as the unique real solutions of Henry equations of P n ( s ) . Some applications to the partial sums of the Riemann zeta function have been also showed.