Character analogue of the Boole summation formula with applications

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CAN M., DAĞLI M. C.

TURKISH JOURNAL OF MATHEMATICS, cilt.41, sa.5, ss.1204-1223, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 5
  • Basım Tarihi: 2017
  • Doi Numarası: 10.3906/mat-1607-23
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1204-1223
  • Anahtar Kelimeler: Boole summation formula, Dirichlet L-function, Hardy Berndt sum, Bernoulli and Euler polynomials, HARDY-BERNDT SUMS, HYBRID MEAN-VALUE, DEDEKIND SUMS, RECIPROCITY FORMULA, TRIGONOMETRIC SUMS, EISENSTEIN SERIES, THETA-FUNCTIONS, RAMANUJAN SUM
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, we present the character analogue of the Boole summation formula. Using this formula, an integral representation is derived for the alternating Dirichlet L-function and its derivative is evaluated at s = 0. Some applications of the character analogue of the Boole summation formula and the integral representation are given about the alternating Dirichlet L-function. Moreover, the reciprocity formulas for two new arithmetic sums, arising from the summation formulas, and for Hardy-Berndt sum S-p, (b, c : x) are proved.