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Writer/Editor: Shivangi Vasudev Bhatt

Photo: Media and Communication, IIT Gandhinagar

In an incredibly proud moment, Prof Atul Dixit, Assistant Professor of Mathematics at IITGN, has become the first Indian mathematician to win the prestigious Gábor Szegö Prize 2021 awarded by the Society of Industrial and Applied Mathematics (SIAM), USA.

The SIAM Activity Group on Orthogonal Polynomials and Special Functions (SIAG/OPSF) awards the Gábor Szegö Prize every two years to one early-career researcher for outstanding research contributions in the area of orthogonal polynomials and special functions. It is for the first time that this prize has been awarded to an Indian mathematician. Prof Atul Dixit has been selected for this award for his “impressive scientific work in solving problems related to number theory using special functions, in particular related to the work of Ramanujan.”

The prize includes a certificate containing the citation. The award was originally supposed to be presented at the 2021 International Symposium on Orthogonal Polynomials, Special Functions, and Applications (OPSFA16). However, due to the current global scenario of the COVID-19 pandemic, the event has been postponed from July 2021 to July 2022. As a part of the award, Prof Atul Dixit will also be invited at the OPSFA16, to be held at the Centre de Recherches Mathematiques (CRM), Universite de Montreal, Canada, to deliver a plenary lecture at the prestigious event.

Prof Atul Dixit’s research in mathematics is at the interface of analytic number theory and special functions. He shares that his work in number theory has led him to discover new interesting special functions such as generalised modified Bessel and Hurwitz zeta functions. Likewise, his work on special functions has frequently had implications in number theory, such as the one on generalised Lambert series or the Voronoï summation formulas. Prof Dixit’s research work has been largely impacted by Srinivasa Ramanujan, who is the main source of inspiration for him.

*I am deeply humbled to know that the SIAM Activity Group on Orthogonal Polynomials and Special Functions (SIAG/OPSF) has chosen me for the 2021 Gábor Szegö prize. I sincerely thank the SIAM prize committee and SIAM for this recognition of my work. I also thank my recommendation letter writers (Professors Bruce Berndt and Nico Temme) for having trust in my work. Receiving this prize also puts more responsibility on my shoulders to do better research than before, and I hope to live up to the expectations put forth on me by SIAM and other well-wishers.*

**Atul Dixit**

##### About Orthogonal Polynomials and Special Functions:

**Special Functions:**

The high-school or college curriculum covers various important functions of Mathematics, such as trigonometric functions, exponential function, logarithm, hyperbolic functions etc. These are called ‘elementary functions’. On the other hand, special functions are ‘non-elementary’ functions, which are equally useful in comparison to the elementary functions, and have numerous applications in various branches of Engineering and Physics. In fact, Professor Richard Askey used to say that ‘special functions’ should actually be called ‘useful functions’. Many special functions have their origins in physics and have emerged from the study of various ordinary and partial differential equations. Some examples of special functions include Gamma function, Bessel functions, Riemann zeta function, Jacobi theta function etc.

**Orthogonal Polynomials:**

Orthogonal polynomials form an important subclass of polynomials which plays an instrumental role in mathematical physics, approximation theory etc. Consider the linear space of polynomials of the real parameter x with real coefficients. If f and g are two elements of this space, we define the inner product of f and g by means of an integral whose integrand consists of a suitable weight function. This inner product is always zero for unequal f and g, hence the nomenclature ‘orthogonal’. Some of the famous orthogonal polynomials are Jacobi polynomials, Hermite polynomials, Laguerre polynomials, Gegenbauer polynomials etc.

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