# 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.

• N. Saradha, More variants of Erd{\H o}s- Selfridge superelliptic curves and their rational points (submitted).

• Pranabesh Das , Shanta Laishram and N. Saradha, Variations of Erd{\H o}s- Selfridge superelliptic curves and their rational points, to appear in Mathematika.

• Ekata Saha and N. Saradha, On interlacing of zeros of some family of modular forms, to appear in J. Number Theory.

• Pranabesh Das , Shanta Laishram and N. Saradha, Cubes in products of terms from an arithmetic progression, to appear in Acta Arithmetica

• N. Saradha and Divyum Sharma , A note on Thue inequalities with few coefficients, to appear in Alladi60 Proceedings

• Shabnam Akhtari, N. Saradha and Divyum Sharma, Thue's inequalities and hypergeometric method, The Ramanujan Journal, DOI 10.1007/s11139-017- 9887-4.

• Mathematica workings of the paper Thue's inequalities and hypergeometric method by Shabnam Akhtari, N. Saradha and Divyum Sharma text file

• N. Saradha and Divyum Sharma , Contributions to a conjecture of Mueller and Schmidt on Thue inequalities, Proceedings- Mathematical Sciences 127 (4), 565-584. DOI 10.1007/s12044-017-0353-4

• N. Saradha, On the length of the period of a real quadratic irrational, Indian J. of Pure and Applied Math-Springer, 48 (3), 311-321. DOI: 10.1007/s13226-017-0229-4

• N. Saradha and Divyum Sharma, Arithmetic nature of Infinite series and Integrals}, Contemporary Mathematics, 655 (2015), 191-207. PDF file

• Lajos Hajdu and N. Saradha, On generalizations of problems of Recaman and Pomerance, J. Number Theory 162 (2016), 552-563. http//dx.doi.org/10.1016/j.jnt.2015.10.006. PDF file

• N. Saradha and Divyum Sharma, Number of solutions of cubic Thue inequalities with positive discriminant, Acta Arith, 171.1(2015), 81-95. PDF file

• F. Luca, N. Saradha and T. N. Shorey, Squares in products of factorials, Monatsh Math 175 (2014), 385-400.\\ DOI: 10.1007/s00605-014-0641-3 PDF file

• N. Saradha and T. N. Shorey, Squares in blocks from an Arithmetic Progression and Galois group of Generalized Laguerre polynomials, Int. J. Number Theory, Vol 11, No.1 (2015) 233-250.\\ DOI:10.1142/S1793042115500141 PDF file

• N. Saradha and Divyum Sharma, Simultaneous rational approximation via Rickert Integrals, Indag Math. 26 (2015) 88-105.\\ available online: http://dx.doi.org/10.1016/j.indag.2014.07.001 PDF file

• N. Saradha and Divyum Sharma, Number of representations of integers by binary forms, Publ.Math.Debrecen 85/1-2 (2014), 233-255; Corrigendum,ibid.86/3-4(2015),503-504. PDF file PDF file

• A. Dujella and N. Saradha, Diophantine $m-$ tuples with elements in arithmetic progressions, Indag Math. 25 (2014),131-136. PDF file

• A. Dujella, F. Najman, N. Saradha and T.N. Shorey, Products of three factorials, Publ. Math. Debrecen 85/1-2 (2014),123-130. PDF file

• A. Sankaranarayanan N. Saradha and Saurabh Kumar Singh, Normality of some decimals generated by primes in a residue class, J. Number Theory, 133 (2013), 1229-1250. PDF file

• L. Hajdu, N. Saradha and R. Tijdeman, On a conjecture of Pomerance, Acta Arith. 155.2 (2012), 175-184. PDF file

• N.Saradha, Application of explicit $abc-$ Conjecture to two Diophantine Equations, Acta Arith. 151 (2012), 401-419. PDF file

• L. Hajdu and N.Saradha, Disproof of a conjecture of Jacobsthal, Math. Comp. 81, No. 280,(2012) 2461-2471. PDF file

• N. Saradha, Conjecture of Pomerance for some even integers and odd primorials, Publ. Math. Debrecen 79/3-4 (2011),699-706. DVI file

• Shabnam Akhtari and N. Saradha, Irreducibility of some orthogonal polynomials , Indag Mathem. 21 (2011), 127-137. PDF file

• L.Hajdu and N. Saradha, On a problem of Recaman and its generalization, J. Number Theory, 131 (2011), 18-24. PDF file

• L. Hajdu and N. Saradha, On a problem of Pillai and its generalizations, Acta Arith. 144 (2010), 323-347. PDF file

• M. Ram Murty and N. Saradha , Euler-Lehmer Constants and a Conjecture of Erdős, J. Number Theory, 130 (2010), 2671-2682. 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.,143 (2010), 211-226. PDF file

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

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

• M. Ram Murty and N.Saradha, Special values of the polygamma functions, Int.J. of Number Theory, 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, 4(3),(2008),475-493. PDF file

• N.Saradha and R.Tijdeman, Arithmetic Progressions with Common Difference Divisible by Small Primes, Acta Arith., 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 $0 PDF file • M. Ram Murty and N. Saradha, Transcendental values of the digamma function, J. Number Theory 125, (2007), 298-318. PDF file • N. Saradha and Anitha Srinivasan, Solutions of some generalised Ramanujan-Nagell equations via binary quadratic forms, Publ. Math. Debrecen, 71/3-4 (2007), 349-374. PDF file • N. Saradha and Anitha Srinivasan, Solutions of some generalised Ramanujan-Nagell equation, Indag. Mathem.,N.S., 17 (1), (2006), 103-114. PDF file • S.D. Adhikari, P. Rath and N. Saradha, On the sets of uniqueness of a distribution function of$\{\xi(p/q)\sp n\}$. Acta Arith. 119 (2005), no. 4, 307--316. 11J71 (11K06) PDF file • K. Győry, L. Hajdu and N. Saradha, Correction to: "On the Diophantine equation$n(n+d)\cdots(n+(k-1)d)=by\sp l$" [Canad. Math. Bull. 47 (2004), no. 3, 373--388; MR2072598 (2005e:11036)]. Canad. Math. Bull. 48 (2005), no. 4, 636. 11D41 • N. Saradha and T. N. Shorey, T. N. Contributions towards a conjecture of Erdős on perfect powers in arithmetic progression. Compos. Math. 141 (2005), no. 3, 541--560. (Reviewer: Yann Bugeaud) 11D61 (11D41) PDF file • K. Győry, L. Hajdu and N. Saradha, On the Diophantine equation$n(n+d)\cdots(n+(k-1)d)=by\sp l$. Canad. Math. Bull. 47 (2004), no. 3, 373--388. (Reviewer: Yuri Bilu) 11D41 • N. Saradha and T. N. Shorey, Almost squares and factorisations in consecutive integers. Compositio Math. 138 (2003), no. 1, 113--124. (Reviewer: K. Győry) 11D57 (11B25) PS file • N. Saradha and T. N. Shorey, Almost squares in arithmetic progression. Compositio Math. 138 (2003), no. 1, 73--111. (Reviewer: K. Győry) 11D57 (11B25 11J86) PS file • N. Saradha and R. Tijdeman, On the transcendence of infinite sums of values of rational functions. J. London Math. Soc. (2) 67 (2003), no. 3, 580--592. 11J81 PS file • S. D. Adhikari, N. Saradha, T. N. Shorey and R. Tijdeman, Transcendental infinite sums. Indag. Math. (N.S.) 12 (2001), no. 1, 1--14. (Reviewer: Yann Bugeaud) 11J81 (11J86) • Saradha, N.; Shorey, T. N. Almost perfect powers in arithmetic progression. Acta Arith. 99 (2001), no. 4, 363--388. (Reviewer: K. Győry) 11D61 (11D41) • Hanrot, G.; Saradha, N.; Shorey, T. N. Almost perfect powers in consecutive integers. Acta Arith. 99 (2001), no. 1, 13--25. (Reviewer: K. Győry) 11D61 (11D41) • Saradha, N.; Shorey, T. N.; Tijdeman, R. Some extensions and refinements of a theorem of Sylvester. Acta Arith. 102 (2002), no. 2, 167--181. (Reviewer: Pieter Moree) 11B25 • Saradha, N. Transcendence measure for$\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, 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