On the solution for the diffusion equation related to the L-functions attached to cusp forms-Reference-Cited by-同舟云学术

On the solution for the diffusion equation related to the L-functions attached to cusp forms

Published:2023 Issue:1 Part B Volume:27 Page:521-526
ISSN:0354-9836
Container-title:Thermal Science
language:en
Short-container-title:THERM SCI

Author:

Yang Xiao-Jun¹,Abdel-Aty Mahmoud²,Hayat Tasawar³

Affiliation:

1. State Key Laboratory for Geo-Mechanics and Deep Underground Engineering, and School of Mathematics, China University of Mining and Technology, Xuzhou, China + Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia + Department of Mathematics, College of Science, Kyung Hee University, Seoul, Republic of Korea

2. Mathematics Department, Faculty of Sciences, Sohag University, Sohag, Egypt + Center for Photonics and Smart Materials (CPSM), Zewail City of Science and Technology, Zewail, Egypt

3. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

Abstract

In this article we suggest the entire functions associated with the L-functions at?tached to cusp forms. The entire function defined by the Fourier cosine transform is the solution for the diffusion equation in 1-D case. We propose three conjectures for the zeros of three entire functions of order one via theory of entire functions.

Publisher

National Library of Serbia

Subject

Renewable Energy, Sustainability and the Environment

Reference8 articles.

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2. Berndt, B. C., Knopp, M. I., Hecke’s Theory of Modular Forms and Dirichlet Series, World Scientific, Singapore, Singapore, 2008, Vol. 5,

3. Ogg, A., Modular Forms and Dirichlet Series, WA Benjamin, New York, USA, 1969, Vol. 39

4. Hafner, J. L., Zeros on the Critical Line for Dirichlet Series Attached to Certain Cusp Forms, Mathematische Annalen, 264 (1983), 1, pp. 21-37

5. De Bruijn, N. G., The Roots of Trigonometric Integrals, Duke Mathematical Journal, 17 (1950), 3, pp. 197-226

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