Mr. Azharuddin Shaik | Number Theory | Best Researcher Award

PhD Scholar at Indian Institute of Information Technology Guwahati, India

Shaik Azharuddin is a promising young mathematician with deep expertise in hypergeometric and Appell series across finite fields, complex numbers, and $p$-adic settings. Currently pursuing his Ph.D. at IIIT Guwahati under Dr. Gautam Kalita, his research explores intricate connections between special functions, algebraic curves (notably elliptic curves), and modular forms. Azharuddin’s scholarly output includes multiple high-impact publications in internationally reputed journals such as The Ramanujan Journal, Research in Number Theory, Finite Fields and Their Applications, and Journal of Mathematical Analysis and Applications. He has also actively participated in major mathematical conferences and international workshops, further enhancing his academic profile.

Publication Profile 

Google Scholar

Educational Background 🎓

• Ph.D. in Mathematics
  Indian Institute of Information Technology (IIIT) Guwahati, India
  (August 2021 – Present)
  Supervisor: Dr. Gautam Kalita
  Thesis: Hypergeometric and Appell series over finite fields and in $p$-adic settings; and their connections to algebraic curves.

• M.Sc. in Mathematics
  University of Mysore, Mysore, India
  (August 2017 – May 2019)

• Integrated B.Sc.Ed. in Mathematics, Physics, and Chemistry
  Regional Institute of Education, Mysore, India
  (August 2013 – July 2017)

Professional Experience 💼

• Ph.D. Research Scholar
  Department of Mathematics, IIIT Guwahati
  (2021 – Present)
  Focused on advanced research in number theory, specifically special functions over various fields and their algebraic and geometric implications.

Research Interests 🔬

• Hypergeometric and Appell series over:

  • Complex numbers

  • Finite fields

  • $p$-adic numbers

• Connections of these series to:

  • Algebraic curves (especially elliptic curves)

  • Modular forms

• Transformations, summation identities, and trace formulas in arithmetic geometry and number theory.

Awards and Honors🏆✨

• CSIR-UGC JRF Qualification — Cleared in June 2020, recognizing academic excellence and research potential in mathematical sciences.

• Indirect Recognition — His co-authored paper in Finite Fields and Their Applications contributed to Dr. Gautam Kalita receiving the A.K. Agarwal Best Publication of the Year 2024 by the Society for Special Functions and their Applications.

Conclusion🌟

Shaik Azharuddin demonstrates significant promise in the field of pure mathematics, particularly number theory and arithmetic geometry. His rigorous academic training, productive research output, and active engagement with international conferences and workshops position him as a rising scholar. With several publications in high-quality journals and a research focus aligned with contemporary mathematical challenges, he is well-prepared to contribute to both academia and collaborative research environments. As he nears the completion of his Ph.D., his profile reflects readiness for advanced research positions or postdoctoral opportunities globally.

Publications 📚

1. 🧮 A family of algebraic curves and Appell series over finite fields
   ✍️ S. Azharuddin, G. Kalita
   📰 The Ramanujan Journal, Vol. 64(3), pp. 823–834
   📅 2024 | 🔗 Cited by: 3

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2. 🔄 Transformations for Appell series over finite fields and traces of Frobenius for elliptic curves
   ✍️ G. Kalita, S. Azharuddin
   📰 Finite Fields and Their Applications, Vol. 92, Article ID: 102301
   📅 2023 | 🔗 Cited by: 3

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3. 🔢 F₄-Appell series in p-adic settings and their connections to algebraic curves
   ✍️ S. Azharuddin, G. Kalita
   📰 Journal of Mathematical Analysis and Applications, Article ID: 129601
   📅 2025 | 📌 Status: Published

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4. ➕ A summation transformation formula for Gaussian hypergeometric series and twisted Kloosterman sheaf sums
   ✍️ G. Kalita, S. Azharuddin, F. Sayed
   📰 Research in Number Theory, Vol. 11(1), Article 22
   📅 2025 | 📌 Status: Published

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5. 🧠 A transformation and certain special values of hypergeometric series over finite fields
   ✍️ G. Kalita, S. Azharuddin
   📰 The Ramanujan Journal, Vol. 66(33), pp. 1–15
   📅 2025 | 📌 Status: Published

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