# 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.

Book: N. Saradha and R. Thangadurai, Pillars of Transcendence,
to be published by Springer Nature.

N. Saradha, Rational points with large denominator on Erdos-Selfridge
super elliptic curves, submitted.

Ekata Saha and N. Saradha, On the interlacing of zeros of Poincare series,
Ramanujan J. https://doi.org/10.1007/s11139-019-00164-x

N. Saradha, More variants of Erd{\H o}s- Selfridge superelliptic curves
and their rational points, Indian J. Pure and Applied Math. 50 (2019),333-342.

A. Berczes, A. Dujella, L. Hajdu, N. Saradha and R. Tijdeman, Products of
factorials which are powers, Acta Arith 190.4 (2019),339-350.
DOI:10.4064/aa171008-16-10

Pranabesh Das , Shanta Laishram and N. Saradha, Variants of
Erd{\H o}s- Selfridge superelliptic curves and their rational points,
Mathematika, 64 (2018), no.2, 380-386.
DOI 10.1112/S0025579317000559.

Ekata Saha and N. Saradha, On interlacing of zeros of some family of
modular forms, J. Number Theory, 183 (2018), 213-232.

Pranabesh Das , Shanta Laishram and N. Saradha, Cubes in products
of terms from an arithmetic progression, Acta Arith. 184 (2018),117-126.

N. Saradha and Divyum Sharma , A note on Thue inequalities with
few coefficients, Analytic Number Theory, modular forms and q-hyper geometric
series, 665-675, Springer, Proc. Math. Stat, 221 , Springer, Cham, 2017.

Shabnam Akhtari, N. Saradha and Divyum Sharma, Thue's inequalities
and hypergeometric method, Ramanujan J., 45 (2018), no.2, 521-567.
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
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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.
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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.
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N.Saradha, Application of explicit $abc-$ Conjecture to two Diophantine
Equations, Acta Arith. 151 (2012), 401-419.
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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.
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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.
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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