Year 2020, Volume 15 , Issue 1, Pages 148 - 157 2020-05-31

Bazı Hardy Toplamları ve Ramanujan Toplamının Ortalama Değeri Hakkında Yeni Bağıntılar
New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum

Muhammet Cihat DAĞLI [1]


Dedekind toplamı, Dedekind eta-fonksiyonunun dönüşüm formülünde doğal olarak ortaya çıkmıştır. Benzer şekilde, Hardy toplamlarına ise theta fonksiyonunun dönüşüm formüllerinde karşılaşılmıştır. Günümüze kadar bu toplamlar, analitik sayılar teorisi (Dedekind η-fonksiyonu), cebirsel sayılar teorisi (sınıf sayıları), latis noktası problemleri, topoloji ve cebirsel geometri alanlarında çok sayıda önemli uygulamalara sahiptir. Bu toplamların çeşitli aritmetik özellikleri birçok bilim adamı tarafından analiz edilmiştir. Son zamanlarda ise, Hardy toplamları, Ramanujan toplamı ve Kloosterman toplamı gibi önemli toplamların sağladığı özellikler göz önüne alınarak, ilginç ve anlamlı özdeşlikler elde edilmiştir. Bu makalede, Hardy toplamları ve Ramanujan toplamına aritmetik açıdan odaklanmaya devam edeceğiz. Daha açık olarak, Dirichlet L-fonksiyonlarının özellikleri yardımıyla Hardy toplamları ve Ramanujan toplamının ortalama değer problemini ele alacağız ve onlar için bazı hesaplama formülleri sunacağız.

Dedekind sum first occured naturally in Dedekind’s transformation law of his eta-function. In analogy, Hardy sums are encountered in the transformation formula of the theta function. Up to now, they have many of remarkable applications in analytic number theory (Dedekind's η-function), algebraic number theory (class numbers), lattice point problems, topology and algebraic geometry. Miscellaneous arithmetical properties of these sums have been analyzed by many scholars. Recently, considering the characteristics of Hardy sums and other celebrated sums such as Ramanujan sum and Kloosterman sum, interesting and meaningful identities have been obtained. In this paper, we continue to focus on arithmetical aspects of Hardy sums and Ramanujan sum. More precisely, we consider a mean value problem of these sums and Ramanujan sum with the help of the features of Dirichlet L-functions and present some computational formulas for them.

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Primary Language en
Subjects Mathematics
Journal Section Makaleler
Authors

Orcid: 0000-0003-2859-902X
Author: Muhammet Cihat DAĞLI (Primary Author)
Institution: AKDENIZ UNIVERSITY
Country: Turkey


Thanks The author would like to thank the anonymous referees for helpful suggestions that improved the paper.
Dates

Publication Date : May 31, 2020

Bibtex @research article { sdufeffd702928, journal = {Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi}, issn = {}, eissn = {1306-7575}, address = {}, publisher = {Süleyman Demirel University}, year = {2020}, volume = {15}, pages = {148 - 157}, doi = {10.29233/sdufeffd.702928}, title = {New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum}, key = {cite}, author = {Dağlı, Muhammet Cihat} }
APA Dağlı, M . (2020). New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum . Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi , 15 (1) , 148-157 . DOI: 10.29233/sdufeffd.702928
MLA Dağlı, M . "New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum" . Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi 15 (2020 ): 148-157 <https://dergipark.org.tr/en/pub/sdufeffd/issue/54573/702928>
Chicago Dağlı, M . "New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum". Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi 15 (2020 ): 148-157
RIS TY - JOUR T1 - New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum AU - Muhammet Cihat Dağlı Y1 - 2020 PY - 2020 N1 - doi: 10.29233/sdufeffd.702928 DO - 10.29233/sdufeffd.702928 T2 - Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi JF - Journal JO - JOR SP - 148 EP - 157 VL - 15 IS - 1 SN - -1306-7575 M3 - doi: 10.29233/sdufeffd.702928 UR - https://doi.org/10.29233/sdufeffd.702928 Y2 - 2020 ER -
EndNote %0 Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum %A Muhammet Cihat Dağlı %T New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum %D 2020 %J Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi %P -1306-7575 %V 15 %N 1 %R doi: 10.29233/sdufeffd.702928 %U 10.29233/sdufeffd.702928
ISNAD Dağlı, Muhammet Cihat . "New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum". Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi 15 / 1 (May 2020): 148-157 . https://doi.org/10.29233/sdufeffd.702928
AMA Dağlı M . New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum. SDÜFEFFD. 2020; 15(1): 148-157.
Vancouver Dağlı M . New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi. 2020; 15(1): 148-157.