DEDEKIND SUMS INVOLVING JACOBI MODULAR FORMS AND SPECIAL VALUES OF BARNES ZETA FUNCTIONS

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Bayad A., ŞİMŞEK Y.

ANNALES DE L INSTITUT FOURIER, cilt.61, sa.5, ss.1977-1993, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 61 Sayı: 5
  • Basım Tarihi: 2011
  • Doi Numarası: 10.5802/aif.2663
  • Dergi Adı: ANNALES DE L INSTITUT FOURIER
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1977-1993
  • Anahtar Kelimeler: Elliptic Dedekind sums, modular forms, theta functions, ellpitic functions, Bernoulli functions, Jacobi modular forms, COTANGENT SUMS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper we study three new shifted sums of Apostol-Dedekind-Rademacher type. The first sums are written in terms of Jacobi modular forms, and the second sums in terms of cotangent and the third sums are expressed in terms of special values of the Barnes multiple zeta functions. These sums generalize the classical Dedekind-Rademacher sums. The main aim of this paper is to state and prove the Dedekind reciprocity laws satisfied by these new sums. As an application of our Dedekind reciprocity law we show how to derive all the well-known results on Dedekind reciprocity law studied by Hall-Wilson-Zagier, Beck-Berndt-Dieter, Katayama and Nagasaka-Ota-Sekine.