Anup Dixit

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I am interested in analytic and algebraic number theory. I work on problems related to families of L-functions, generalized Brauer-Siegel conjecture, infinite extensions of number fields, universality of L-functions, Euler-Kronecker constants, Diophantine geometry and probabilistic number theory.

Publications/Pre-prints

  1. The Lindelof class of L-functions, PhD Thesis, University of Toronto, 2018.

  2. Uniqueness results for a class of L-functions, GANITA: Conference on Geometry, Algebra, Number Theory and their Information Technology Applications, Springer Proceedings in Mathematics and Statistics, , 163-181, (2018).

  3. The Lindelof class of L-functions II (with V. K. Murty), International Journal of Number Theory, 15, no. 10, 2201-2221, (2019).

  4. On the Selberg class of L-functions, Proceedings of Ropar Conference, RMS- Lecture Notes series, No. 26, 21-42, (2020).

  5. On Euler-Kronecker constants and the generalized Brauer-Siegel theorem, Proceedings of AMS, 148, 1399-1414, (2020).

  6. A Uniqueness property of general Dirichlet series, Journal of number theory, 206, 123-137, (2020).

  7. A localized Erdos-Kac theorem, (with M. R. Murty), Hardy-Ramanujan journal, 43 , 17-23, (2020).

  8. On Large values of a class of L-functions on the 1-line (with K. Mahatab), Bulletin of Australian Mathematical Society, 103, no. 2, 230-243, (2021).

  9. On the Generalized Brauer-Siegel Theorem for asymptotically exact families with solvable Galois closure, International Mathematics Research Notices (IMRN), 2021 , issue 14, 10941-10956, (2021).

  10. On the generalised Diophantine m-tuples, (with S. Kim and M. R. Murty), Proceedings of AMS , 150 , no. 4, 1455-1465, (2022).

  11. On limit theorem of zeta-functions , Proceedings of Subbarao conference, to appear.

  12. A localized Erdos-Kac theorem for omega_y(p+a) , (with M. R. Murty), Hardy-Ramanujan journal , 45,74-83, (2022).

  13. On Ihara's conjectures for Euler-Kronecker constants , (with M. R. Murty), Acta Arithmetica, 210, 95-123, (2023). Errata

  14. An effective bound on generalized Diophantine m-tuples, (with S. Bhattacharjee and D. Saikia), Bulletin of Australian Math. Soc., 109, Issue 2, 242-253, (2024).

  15. Linear independence of values of the q-exponentials and related functions, (with V. Kumar and S. Pathak), Bulletin of Australian Math. Soc., 109 , Issue 3, 453-463, (2024).

  16. Lower bound heights of algebraic numbers and low lying zeros of Dedekind zeta function, (with S. Kala), submitted .

  17. A consequence of Tate's conjecture on the order of pole of certain L-functions, (with V. K. Murty), submitted.

  18. A function related to the Mordell-Weil rank of elliptic curves, (with M. R. Murty and S. Pathak), International Journal of number theory, 20, no. 9, 2267-2275, (2024).

  19. On the distribution of phi(sigma(n)), (with S. Bhattacharjee), Integers, 24, A65, (2024).

  20. On points of small height in infinite extensions, (with S. Kala), Annali della Scuola Normale Superiore di Pisa, to appear.

  21. A p-adic criterion for Lehmer's conjecture,(with S. Kala), International Journal of number theory, to appear.

  22. Zeta-functions on infinite extensions, submitted.

  23. How often are [n^a] and [n^b] simultaneously primes, Ramanujan Journal, to appear.

  24. On the zero-free region of Artin L-functions over almost S_n-fields, submitted .

  25. Statistics of the genus number for S_3 x C_q and D_4-fields, submitted .

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