Publications of N. Saradha

  • Diophantine Equations, Editor: N. Saradha, Narosa Publishing House, New Delhi, India. This is the Proceedings of a conference held at Tata Institute of Fundamental Research, Mumbai in December 2005 to honour Professor T. N. Shorey on his 60th birthday.

  • L.Hajdu and N. Saradha, On a problem of Recaman and its generalization, to appear in J. Number Theory. PDF file

  • L. Hajdu and N. Saradha, On a problem of Pillai and its generalizations, to appear in Acta Arithmetica. PDF file

  • M. Ram Murty and N. Saradha , Euler-Lehmer Constants and a Conjecture of Erdős, to appear in J. Number Theory. PDF file

  • Carrie E. Finch and N. Saradha, On the irreducibility of certain polynomials with coefficients that are products of terms in an arithmetic progression, Acta Arith.,{\bf 143} (2010), 211-226. PDF file

  • N. Saradha and T. N. Shorey, Almost perfect powers in consecutive integers (II), Indag Mathem., N.S., {\bf 19} (4) (2009), 649-658. PDF file

  • M. Ram Murty and N. Saradha {\it Transcendental values of the p-adic digamma function}, Acta Arith., {\bf 133},(2008), 349-362. PDF file

  • M. Ram Murty and N.Saradha, Special values of the polygamma functions, Int.J. of Number Theory, {\bf 5}, No. 2 (2009), 257-270. PDF file

  • A. Sankaranarayanan and N. Saradha, Estimates for the solutions of certain Diophantine equations by Runge's method, Int. J. of Number Theory,{\bf 4}(3),(2008),475-493. PDF file

  • N.Saradha and R.Tijdeman, Arithmetic Progressions with Common Difference Divisible by Small Primes, Acta Arith., {\bf 131},(2008), 267-279. PS file

  • N. Saradha and T. N. Shorey, On the equation $$n(n+d) \cdots (n+(i_0-1)d)(n+(i_0+1)d) \cdots (n+(k-1)d))=y^\ell$$ with $0 PDF file

  • M. Ram Murty and N. Saradha, Transcendental values of the digamma function, J. Number Theory {\bf 125}, (2007), 298-318. PDF file

    PDF file of the published version.

  • N. Saradha and Anitha Srinivasan, Solutions of some generalised Ramanujan-Nagell equations via binary quadratic forms, Publ. Math. Debrecen,{\bf 71/3-4} (2007), 349-374. PDF file

  • Saradha, N.; Anitha Srinivasan, Solutions of some generalised Ramanujan-Nagell equation, Indag. Mathem.,N.S., 17 (1), (2006), 103-114. PDF file

  • Adhikari, S. D.; Rath, P.; Saradha, N. On the sets of uniqueness of a distribution function of $\{\xi(p/q)\sp n\}$. Acta Arith. 119 (2005), no. 4, 307--316. 11J71 (11K06) PDF file

  • Győry, K.; Hajdu, L.; Saradha, N. Correction to: "On the Diophantine equation $n(n+d)\cdots(n+(k-1)d)=by\sp l$" [Canad. Math. Bull. 47 (2004), no. 3, 373--388; MR2072598 (2005e:11036)]. Canad. Math. Bull. 48 (2005), no. 4, 636. 11D41

  • Saradha, N.; Shorey, T. N. Contributions towards a conjecture of Erdös on perfect powers in arithmetic progression. Compos. Math. 141 (2005), no. 3, 541--560. (Reviewer: Yann Bugeaud) 11D61 (11D41) PDF file

  • Győry, K.; Hajdu, L.; Saradha, N. On the Diophantine equation $n(n+d)\cdots(n+(k-1)d)=by\sp l$. Canad. Math. Bull. 47 (2004), no. 3, 373--388. (Reviewer: Yuri Bilu) 11D41

  • Saradha, N.; Shorey, T. N. Almost squares and factorisations in consecutive integers. Compositio Math. 138 (2003), no. 1, 113--124. (Reviewer: K. Győry) 11D57 (11B25) PS file

  • Saradha, N.; Shorey, T. N. Almost squares in arithmetic progression. Compositio Math. 138 (2003), no. 1, 73--111. (Reviewer: K. Győry) 11D57 (11B25 11J86) PS file

  • Saradha, N.; Tijdeman, R. On the transcendence of infinite sums of values of rational functions. J. London Math. Soc. (2) 67 (2003), no. 3, 580--592. 11J81 PS file

  • Adhikari, S. D.; Saradha, N.; Shorey, T. N.; Tijdeman, R. Transcendental infinite sums. Indag. Math. (N.S.) 12 (2001), no. 1, 1--14. (Reviewer: Yann Bugeaud) 11J81 (11J86)

  • Saradha, N.; Shorey, T. N. Almost perfect powers in arithmetic progression. Acta Arith. 99 (2001), no. 4, 363--388. (Reviewer: K. Győry) 11D61 (11D41)

  • Hanrot, G.; Saradha, N.; Shorey, T. N. Almost perfect powers in consecutive integers. Acta Arith. 99 (2001), no. 1, 13--25. (Reviewer: K. Győry) 11D61 (11D41)

  • Saradha, N.; Shorey, T. N.; Tijdeman, R. Some extensions and refinements of a theorem of Sylvester. Acta Arith. 102 (2002), no. 2, 167--181. (Reviewer: Pieter Moree) 11B25

  • Saradha, N. Transcendence measure for $\eta/\omega$. Acta Arith. 92 (2000), no. 1, 11--25. (Reviewer: Michel Waldschmidt) 11J82 (11J81)

  • Saradha, N.; Shorey, T. N. The equation $(x\sp n-1)/(x-1)=y\sp q$ with $x$ square. Math. Proc. Cambridge Philos. Soc. 125 (1999), no. 1, 1--19. (Reviewer: Yann Bugeaud) 11D61 (11J86)

  • Saradha, N.; Shorey, T. N.; Tijdeman, R. Corrections to the paper: "On values of a polynomial at arithmetic progressions with equal products" [Acta Arith. 72 (1995), no. 1, 67--76; MR 96j:11041]. Acta Arith. 84 (1998), no. 4, 385--386. (Reviewer: István Gaál) 11D75 (11C08 11D41)

  • Saradha, N. Squares in products with terms in an arithmetic progression. Acta Arith. 86 (1998), no. 1, 27--43. (Reviewer: Yuri Bilu) 11D61 (11B25 11B57 11D41)

  • Saradha, N. On perfect powers in products with terms from arithmetic progressions. Acta Arith. 82 (1997), no. 2, 147--172. (Reviewer: Nikos Tzanakis) 11D61

  • Saradha, N. On blocks of arithmetic progressions with equal products. J. Théor. Nombres Bordeaux 9 (1997), no. 1, 183--199. (Reviewer: Yuri Bilu) 11B25 (11D41 11J86)

  • Saradha, N.; Shorey, T. N.; Tijdeman, R. On values of a polynomial at arithmetic progressions with equal products. Acta Arith. 72 (1995), no. 1, 67--76. (Reviewer: IstvánGaál) 11D75 (11C08 11D41)

  • Saradha, N.; Shorey, T. N.; Tijdeman, R. On arithmetic progressions with equal products. Acta Arith. 68 (1994), no. 1, 89--100. (Reviewer: C. L. Stewart) 11D41 (11B25)

  • Saradha, N.; Shorey, T. N.; Tijdeman, R. On the equation $x(x+1)\cdots (x+k-1)=y(y+d)\cdots (y+(mk-1)d), m=1,2$. Acta Arith. 71 (1995), no. 2, 181--196. (Reviewer: David Lee Hilliker) 11D41

  • Saradha, N.; Shorey, T. N.; Tijdeman, R. On arithmetic progressions of equal lengths with equal products. Math. Proc. Cambridge Philos. Soc. 117 (1995), no. 2, 193--201. (Reviewer: D. R. Heath-Brown) 11D57 (11D41)

  • Saradha, N.; Shorey, T. N. On the equation $x(x+d\sb 1)\cdots(x+(k-1)d \sb 1)=y(y+d\sb 2)\cdots(y+(mk-1)d\sb 2)$. K. G. Ramanathan memorial issue. Proc. Indian Acad. Sci. Math. Sci. 104 (1994), no. 1, 1--12. (Reviewer: F. Beukers) 11D41 (11D57)

  • Murty, M. Ram; Saradha, N. An asymptotic formula by a method of Selberg. C. R. Math. Rep. Acad. Sci. Canada 15 (1993), no. 6, 273--277. (Reviewer: Qi Yao) 11N25

  • Pinner, C. G.; van der Poorten, A. J.; Saradha, N. Some infinite products with interesting continued fraction expansions. J. Théor. Nombres Bordeaux 5 (1993), no. 1, 187--216. (Reviewer: Cornelis Kraaikamp) 11J70 (11A55)

  • Saradha, N.; Shorey, T. N. On the equation $x(x+d)\cdots(x+(k-1)d)= y(y+d)\cdots(y+(mk-1)d)$. Indag. Math. (N.S.) 3 (1992), no. 2, 237--242. (Reviewer: Nikos Tzanakis) 11D41

  • Saradha, N.; Shorey, T. N. On the equation $(x+1)\cdots(x+k)=(y+1) \cdots(y+mk)$. Indag. Math. (N.S.) 3 (1992), no. 1, 79--90. (Reviewer: K. Győry) 11D41 (11D57)

  • Saradha, N.; Shorey, T. N. The equations $(x+1)\cdots(x+k)=(y+1)\cdots (y+mk)$ with $m=3,4$. Indag. Math. (N.S.) 2 (1991), no. 4, 489--510. (Reviewer: Nikos Tzanakis) 11D57 (11Y50)

  • Saradha, N.; Shorey, T. N. On the ratio of two blocks of consecutive integers. Proc. Indian Acad. Sci. Math. Sci. 100 (1990), no. 2, 107--132. (Reviewer: Nikos Tzanakis) 11D57 (11J86)

  • Murty, M. Ram; Murty, V. Kumar; Saradha, N. Modular forms and the Chebotarev density theorem. Amer. J. Math. 110 (1988), no. 2, 253--281. (Reviewer: Jannis A. Antoniadis) 11F25 (11R45)

  • Murty, M. Ram; Saradha, N. On the sieve of Eratosthenes. Canad. J. Math. 39 (1987), no. 5, 1107--1122. (Reviewer: G. Greaves) 11N60 (11N35)

    Publications in Proceedings



  • N.Saradha and R. Thangadurai, Pillai's problem on consecutive integers, to appear in the Proceedings of the conference on Number Theory and Cryptography held in Harishchandra Research Institute, Allahabad, February, 2007, 176-188. PDF file

  • N. Saradha and Anitha Srinivasan, Generalized Lebesgue-Ramanujan-Nagell Equations, (2008), 207-223, Diophantine Equations, Editor: N. Saradha, Narosa Publishing House, New Delhi, India. PDF file

  • On non vanishing infinite sums, The Riemann zeta function and Related themes: Papers in honour of Professor K. Ramachandra, Ramanujan Mathematical Society, Lecture Notes Series, {\bf 2} (2006),pp.121-129. PDF file

  • Chowla's problem on the non-vanishing of certain infinite series and related questions to appear in Proceedings of the conference in honour of R. P. Bambah on his 80th birthday. PDF file

    Publications elsewhere



  • Transcendence I, Bulletin, Bombay Mathematical Colloquium, 1998, vol 14,nos 1-2, 26-34. DVI file

  • Transcendence II, Bulletin, Bombay Mathematical Colloquium, 1998, vol 14,no 3, 27-36. DVI file

  • S.D.Adhikari and N. Saradha , Arithmetic Nature of Sums of Certain Convergent Series, Resonance, Vol 7, No.11 (2002), 35-46. DVI file