SELECTED PUBLICATIONS WITH LINKS TO PDF FILES

Complete List of Publications (pdf)

118. Ramanujan's class invariants with applications to the vaules of q-continued fractions and theta functions (with H. H. Chan and L.-C. Zhang), in Special Functions, q-Series, and Related Topics, M. Ismail, D. Masson, and M. Rahman, eds., Fields Institute Communication Series, Vol. 14, American Mathematical Society, Providence, RI, 1997, pp. 37-53, (ps).

121. Ramanujan's association with radicals in India (with H. H. Chan and L.-C. Zhang), Amer. Math. Monthly 104 (1997), 913-919, (ps).

122. An overview of Ramanujan's notebooks, in Charlemagne and His Heritage: 1200 Years of Civilization and Science in Europe, Volume 2: Mathematical Arts, P. L. Butzer, H. Th. Jongen, and W. Oberschelp, editors, Brepols, Turnhout, 1998, pp. 119-146, (ps).

123. The remaining 40% of Ramanujan's lost notebook, in Number Theory and its Applications, Surikaisekikenkyuusho Kokyuuroku, No. 1060, RIMS Kyoto University, Kyoto, 1998, pp. 111-118, (Unrefereed Paper) (ps).

124. Radicals and units in Ramanujan's work (with H. H. Chan and L.-C. Zhang), Acta Arith. 87 (1998), 145-158, (ps).

126. Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary (with K. Ono), Sem. Lotharingien de Combinatoire 42 (1999), 63 pp.; in The Andrews Festschrift, D. Foata and G.-N. Han, eds., Springer-Verlag, Berlin, 2001, pp. 39-110, (ps).

127. The Rogers-Ramanujan continued fraction (with H. H. Chan, S.-S. Huang, S.-Y. Kang, J. Sohn, and S. H. Son), J. Comput. Appl. Math. 105 (1999), 9-24, (ps).

130. Ramanujan and the modular j-invariant (with H. H. Chan), Canad. Math. Bull. 42 (1999), 427-440, (ps).

132. The Brocard--Ramanujan diophantine equation n! + 1 = m^2 (with W. Galway), The Ramanujan J. 4 (2000), 41-42, (ps).

133. Eisenstein series in Ramanujan's lost notebook (with H. H. Chan, J. Sohn, and S. H. Son), The Ramanujan J. 4 (2000), 81-114, (ps).

134. Some theorems on the Rogers-Ramanujan continued fraction in Ramanujan's lost notebook (with S.-S. Huang, J. Sohn, and S. H. Son), Trans. Amer. Math. Soc. 352 (2000), 2157--2177, (ps).

135. Incomplete elliptic integrals in Ramanujan's lost notebook (with H. H. Chan and S.-S. Huang), in q-series from a Contemporary Perspective, M. E. H. Ismail and D. Stanton, eds., American Mathematical Society, Providence, RI, 2000, pp. 79-126, (ps).

139. Eisenstein series and approximations to pi (with H. H. Chan), Illinois J. Math. 45 (2001), 75-90, (ps).

140. Flowers which we cannot yet see growing in Ramanujan's garden of hypergeometric series, elliptic functions, and q's, in Special Functions 2000: Current Perspective and Future Directions (J. Bustoz, M. E. H. Ismail, and S. K. Suslov, eds.), Kluwer, Dordrecht, 2001, pp. 61-85, (ps).

141. On the transformation formula for the Dedekind eta-function (with K. Venkatachaliengar), Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, F. G. Garvan and M. E. H. Ismail, eds., Kluwer, Dordrecht, 2001, pp. 73-77, (ps).

142. Formulas of Ramanujan for the power series coefficients of certain quotients of Eisenstein series (with P. R. Bialek and A. J. Yee), International Mathematics Research Notices 21 (2002), 1077-1109, (ps).

143. A certain quotient of eta-functions found in Ramanujan's lost notebook (with H. H. Chan, S.-Y. Kang, and L.-C. Zhang), Pacific J. Math. 202 (2002), 267-304, (ps).

144. Asymptotic formulas for two continued fractions in Ramanujan's lost notebook (with J. Sohn), J. London Math. Soc. (2) 65 (2002), 271-284, (ps).

147. Congruences for the coefficients of quotients of Eisenstein series (with A. J. Yee), Acta Arith. 104 (2002), 297-308, (ps).

148. Integrals of Eisenstein series and derivatives of L-functions, (with S. Ahlgren, A. J. Yee, and A. Zaharescu), International Mathematics Research Notices 2002, No. 32, 1723-1738, (ps).

149. A multi-variable theta product (with A.Zaharescu), Indag. Math. N. S. 13 (2002), 11-22, (ps).

150. An integral of Dedekind eta-functions in Ramanujan's lost notebook (with A. Zaharescu), J. Reine Angew. Math. 551 (2002), 33-39, (ps).

151. Explicit evaluations and reciprocity theorems for finite trigonometric sums (with B. P. Yeap), Advances in Appl. Math., Adv. In Appl. Math. 29 (2002), 358-385, (ps).

152. Commentary on an unpublished lecture by G. N. Watson on solving the quintic (with B. K. Spearman and K. S. Williams), Math. Intell. 24, No. 4 (2002), 15-33, (ps).

153. Ramanujan's contributions to Eisenstein series, especially in his lost notebook (with A. J. Yee), in Number Theoretic Methods - Future Trends, C. Jia and S. Kanemitsu, eds., Kluwer, Dordrecht, 2002, pp. 31-53; abridged version, A survey on Eisenstein series in Ramanujan's lost notebook (with A. J. Yee), in New Aspects of Analytic Number Theory, Y. Tanigawa, ed., Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 2002, pp. 130--141, (ps).

154. On Ramanujan's continued fraction for  (q2; q3)inf/(q;q3)inf (with G. E. Andrews, J. Sohn, A. J. Yee, and A. Zaharescu), Trans. Amer. Math. Soc. 355 (2003), 2397-2411, (ps).

155. A page on Eisenstein series in Ramanujan's lost notebook (with A. J. Yee), Glasgow Math. J. 45 (2003), 123-129 (ps).

156. On the parity of partition functions (with A. J. Yee and A. Zaharescu), Internat. J. Math. 14 (2003), 437-459.

157. A quasi-theta product in Ramanujan's lost notebook (with H. H. Chan and A. Zaharescu), Math. Proc. Cambridge Philos. Soc. 135 (2003), 11-18 (ps).

158. Theorems on partitions from a page in Ramanujan's lost notebook (with A. J. Yee and J. Yi), J. Compo Appl. Math. 160 (2003), 53-68 (ps).

159. The life and work of R. A. Rankin (1915-2001) (with W. Kohnen and K. Ono), Ramanujan J. 7 (2003), 9-38 (ps).

    a. Articles of Rankin, (ps).
    b. Books of Rankin, (ps).
    c. Booksedited of Rankin, (ps).
    d. Obituary and Biographical Notices of Rankin, (ps).
    e. Other Writings of Rankin, (ps).

160. On the generalized Rogers-Ramanujan continued fraction (with A. J. Yee), Ramanujan J. 7 (2003), 321-331 (ps).

161. Combinatorial proofs of identities in Ramanujan's lost notebook associated with the Rogers-Fine identity and false theta functions (with A. J. Yee), Annals of Combinatorics, 7 (2003), 409-423, (ps).

162. A new identity for (q; q)10/inf with an application to Ramanujan's partition congruence modulo 11 (with S. H. Chan, Z.-G. Liu, and H. Yesilyurt), Quart. J. Math. (Oxford) 55 (2004), 13-30 (ps).

163. Two exams taken by Ramanujan in India (with C. A. Reddi), Amer. Math. Monthly 111 (2004), 330-339 (ps).

164. New theorems on the parity of partition functions (with A. J. Yee and A. Zaharescu), J. Reine Angew. Math. 566 (2004), 91-109.

165. An unpublished manuscript of Ramanujan on infinite series identities, J. Ramanujan Math. Soc. 19 (2004), 57-74 (ps).

166. Some integrals in Ramanujan's lost notebook, Proc. Amer. Math. Soc. 132 (2004), 2983-2988 (ps).

167. Finite trigonometric sums and class numbers (with A. Zaharescu), Math. Ann. 330 (2004), 551-575 (ps).

168. q-Gauss summation via Ramanujan and combinatorics (with A. J. Yee), South East Asian J. Math. and Math. Sci. 3 (2004), 15-22 (ps).

169. Cranks and dissections in Ramanujan's lost notebook (with H. H. Chan, S. H. Chan, and W.C. Liaw), J. Combin. Thy. (A) 109 (2005), 91-120 (ps).

170. Ramanujan and cranks (with H. H. Chan, S. H. Chan, and W.C. Liaw), in Theory and Applications of Special Functions. A Volume Dedicated to Mizan Rahman, M. E. H. Ismail and E. Koelink, eds., Springer, Dordrecht, 2005, pp. 77-98. (ps).

171. Continued fractions with three limit points (with G. E. Andrews, J. Sohn, A. J. Yee, and A. Zaharescu), Adv. in Math. 192 (2005), 231-258 (ps).

172. A continued fraction from Ramanujan's lost notebook (with G. Choi), Aequa. Math. 69 (2005), 257-262 (ps).

173. Determinations of analogues of Gauss sums and other trigonometric sums (with M. Beck, O.-Y. Chan, and A. Zaharescu), Internat. J. Number Thy. 1 (2005), 333-356 (pdf).

174. On the power series coefficients of certain quotients of Eisenstein series (with P. R. Bialek), Trans. Amer. Math. Soc. 357 (2005), 4379-4412 (ps).

175. New identities for the Rogers-Ramanujan functions, (with H. Yesilyurt), Acta Arith. 120 (2005), 395-413 (pdf).

176. Weighted divisor sums and Bessel function series (with A. Zaharescu), Math. Ann. 335 (2006), 249-283 (pdf).

178. A reciprocity theorem for certain q-series found in Ramanujan's lost notebook (with S. H. Chan, B. P. Yeap, and A. J. Yee), Ramanujan J., 13 (2007), 27-37 (pdf).

180. Partition identities and Ramanujan's modular equations (with N. D. Baruah), J. Comb. Thy. (A) 114 (2007), 1024-1045 (pdf).

181. Partition-Theoretic Interpretations of Certain Modular Equations of Schroter, Russell and Ramanujan, Annals of Combinatorics 11 (2007), 115-125 (pdf).

183. Sixth order mock theta functions (with S. H. Chan), Adv. Math. 216 (2007), 771-786 (pdf).

184. Ramanujan's congruences for the partition function modulo 5, 7, and 11, Internat. J. Number Thy. 3 (2007), 349-354 (pdf).

185. An identity for the Dedekind eta-function involving two independent complex variables (with W. B. Hart), Bull. London Math. Soc. 39 (2007), 345-347 (pdf).

186. Your hit Parade - The top ten most fascinating formulas from Ramanujan's lost notebook (with G. E. Andrews), Notices, Amer. Math. Soc. 55 (2008), 18-30; abridged version, The five strangest, most fascinating, most interesting results in Ramanujan's lost notebook, to appear (pdf).

187. Ramanujan's series for 1/π arising from his cubic and quartic theories of elliptic functions (with N. D. Baruah), J. Math. Anal. Applics. 341 (2008), 357-371 (pdf).

188. Questionable claims found in Ramanujan's lost notebook (with O.-Y. Chan, S.-G. Lim, and A. Zaharescu), in Tapas in Experimental Mathematics, T. Amdeberhan and V. H. Moll, eds., Contemp. Math., vol. 457, American Mathematical Society, Providence, RI, 2008, pp. 69-98 (pdf).

189. Partition identities arising from theta function identities (with N. D. Baruah), Acta Math. Sinica 24 (2008), 955-970 (pdf).

190. Koshliakov's formula and Guinand's formula in Ramanujan's lost notebook (with Y. Lee and J. Sohn), in Surveys in Number Theory, K. Alladi, ed., Springer, New York, 2008, pp. 21-42 (pdf).

191. A Fragment on Euler's Constant in Ramanujan's Lost Notebook (with T. Huber), South East Asian J. Math. and Math. Sci. 6 (2008), 17-22 (pdf).

192. Ramanujan's series for 1/π: A survey (with N. D. Baruah and H. H. Chan), Math. Student (Special Centenary Volume 2007), 1-24; Amer. Math. Monthly 116 (2009), 567-587 (pdf).

193. A reciprocity theorem for certain hypergeometric series (with D. Koukoulopoulos), Proc. Amer. Math. Soc. 601 (2009), 2369-2373 (pdf).

194. An Integral Analogue of Theta Functions and Gauss Sums in Ramanujan's Lost Notebook (with P. Xu), Math. Proc. Cambridge Philos. Soc. 147 (2009), 257-265 (pdf).

195. Ramanujan's Eisenstein Series and new hypergeometric-like series for 1/π2 (with N. D. Baruah), J. Aprox. Thy. 160 (2009), 135-153 (pdf).

196. Ramanujan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions (with B. Kim and A. J. Yee), J. Comb. Thy. Ser. A, 117 (2010), 957-973 (pdf).

197. A transformation formula involving the Gamma and Riemann zeta functions in Ramanujan's lost notebook (with A. Dixit), in The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, K. Alladi, J. Klauder, and C. R. Rao, eds, Springer, 2010,
pp. 199-210.(pdf).

198. Cranks -- Really the final problem (with H. H. Chan, S. H. Chan, and W.-C. Liaw), Ramanujan J. 23 (2010), 3-15 (pdf).

199. Eisenstein series and Ramanujan-type series for 1/π (with N. D. Baruah), Ramanujan J. 23 (2010), 17-44 (pdf).

200. What is a q-series?, in Ramanujan Rediscovered: Proceedings of a Conference on Elliptic Functions, Partitions, and q-Series in memory of K. Venkatachaliengar: Bangalore, 1-5 June, 2009, N. D. Baruah, B. C. Berndt, S. Cooper, T. Huber, and M. J. Schlosser, eds., Ramanujan Mathematical Society, Mysore, 2010, pp. 31-51 (pdf).

201. A proof of the general theta transformation formula (with C. Gugg, S. Kongsiriwong, and J. Thiel), in Ramanujan Rediscovered: Proceedings of a Conference on Elliptic Functions, Partitions, and q-Series in memory of K. Venkatachaliengar: Bangalore, 1-5 June, 2009, N. D. Baruah, B. C. Berndt, S. Cooper, T. Huber, and M. J. Schlosser, eds., Ramanujan Mathematical Society, Mysore, 2010, pp. 53-62. (pdf).

202. On sums of powers in Ramanujan's lost notebook (with D. Schultz), Applic. Anal. 90 (2011), 725-730 (pdf).

203. Character analogues of theorems of Ramanujan, Koshliakov, and Guinand (with A. Dixit and J. Sohn), Adv. Appl. Math. 46 (2011), 54-70 (pdf).

204. Ramanujan reaches his hand from his grave to snatch your theorems from you, Asia Pacific Math. Newsletter, Asia Pacific Mathematics Newsletter 1, no. 2 (2011), 8-13. (Unrefereed Paper) (pdf).

205. Asymptotic expansions of certain partial theta functions (with B. Kim), Proc. Amer. Math. Soc. 139 (2011), 3779--3788. (pdf).

206. The chief accountant and mathematical friend of Ramanujan -- S. Narayana Aiyar, Amer. Math. Monthly 118 (2011), 765--774. (pdf).

207. Ramanujan's elementary method in partition congruences (with C. Gugg and S. Kim), in Partitions, q-Series and Modular Forms, K. Alladi and F. Garvan, eds., Developments in Math. 23, Springer, New York, 2011, pp. 13--22. (pdf).

208. Weighted divisor sums and Bessel function series, II (with S. Kim and A. Zaharescu), Adv. Math. 229 (2012), 2055--2097. (pdf).

209. Two Dirichlet series evaluations found on page 196 of Ramanujan's lost notebook (with H. H. Chan and Y. Tanigawa), Math. Proc. Cambridge Philos. Soc. 153 (2012), 341--360. (pdf).

210. Weighted divisor sums and Bessel function series, IV (with S. Kim and A. Zaharescu), submitted for publication (pdf).

211. Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi (with G. Lamb and M. Rogers), Ramanujan J. 29 (2012), 185--198. (pdf).

212. Ramanujan's earlier notebooks and his lost notebook, Notices Amer. Math. Soc. 59 (2012), 1531--1534. (mildly refereed) (pdf).

213. Discarded fragments from Ramanujan's papers (with P. Pongsriiam), in Analytic and Probabilistic Methods in Number Theory: Kubilius Memorial Volume, Proceedings of the Fifth International Conference in Honour of J. Kubilius, Palanga, Lithuania, 4--10 September 2011, A. Laurin\v{c}ikas, E. Manstavi\v{c}ius, and G. Stepanauskas, eds., TEV, Vilnius, 2012, pp. 49--59. (pdf).

214. The circle and divisor problems, and double series of Bessel functions (with S. Kim and A. Zaharescu), Adv. Math. 236 (2013), 24--59.(pdf).

215. A problem in diophantine approximation found in Ramanujan's lost notebook (with S. Kim), Ramanujan J. 31 (2013), 83--95.(pdf).

216. Euler products in Ramanujan's lost notebook (with B. Kim and K. S. Williams), Internat. J. Number Thy. 9 (2013), 1313--1349. (pdf).

217. Diophantine approximation of the exponential function and Sondow's conjecture (with S. Kim and A. Zaharescu), Adv. Math. 248 (2013), 1298--1331.(pdf).

218. Lecture given by B. M. Wilson, University of Leeds, May, 1927, Mathematics Newsletter, Ramanujan Mathematical Society 24, No. 1 (2013), 1--6.(pdf).

219. Weighted divisor sums and Bessel function series, III (with S. Kim and A. Zaharescu), J. Reine Angew. Math. 683 (2013), 67--96. (pdf).

220. The circle and divisor problems, and Ramanujan's contributions through Bessel function series, (with S. Kim and A. Zaharescu), in The Legacy of Srinivasa Ramanujan: Proceedings of an International Conference in Celebration of the 125th Anniversary of Ramanujan's Birth: University of Delhi, 17--22 December 2012, B. C. Berndt and D. Prasad, eds., Ramanujan Mathematical Society, Mysore, 2013, pp. 111--127.(pdf).

221. Dirichlet $L$-functions, elliptic curves, hypergeometric functions, and rational approximation with partial sums of power series (with S. Kim and A. Zaharescu), Math. Res. Letters 20 (2013), 429--448. (pdf).

222. Diophantine approximation with partial sums of power series (with S. Kim, M.Tip Phaovibul, and A. Zaharescu), Acta Arith. 161 (2013), 249--266. (pdf).

223. Ramanujan, his lost notebook, its importance, in Navigating across Mathematical Cultures and Times, I. M. Vandoulakis and L. Dun, eds., World Scientific Press, to appear. (pdf).

224. Analogues of Koshliakov's formula (with S. Kim and A. Zaharescu), Ramanujan 125, K. Alladi, F. Garvan, and A. J. Yee, eds., Contemporary Mathematics, vol. 627, American Mathematical Society, Providence, RI, 2014, to appear. (pdf).

225. Identities for partitions with distinct colors (with R. R. Zhou), Ann. Combin., to appear. (pdf).

226. On a secant Dirichlet series and Eichler integrals of Eisenstein series (with A. Straub), submitted for publication. (pdf).

227. Proofs of conjectures of Sandon and Zanello on colored partition identities (with R. R. Zhou), J. Korean Math. Soc., to appear. (pdf).

228. Weighted divisor sums and Bessel Function Series, V (with S. Kim and A. Zaharescu), J. Approx. Thy., to appear. (pdf).

229. Finite and infinite Rogers--Ramanujan continued fractions in Ramanujan's lost notebook (with S.--Y. Kang and J. Sohn, submitted for publication. (pdf).

230. Logarithmic means and double series of Bessel functions (with S. Kim), submitted for publication. (pdf).

 

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Books:

  • Ramanujan: Essays and Surveys (with R. A. Rankin), American Mathematical Society, Providence, RI, 2001; jointly published by the London Mathematical Society, London, 2001.
  • Ramanujan's Lost Notebook, Part I (with G.E. Andrews), Springer, New York (2005).
  • Number Theory in the Spirit of Ramanujan, American Mathematical -- --Society, Providence, RI 2006.
  • Hecke's Theory of Modular Forms and Dirichlet Series (with M. I. Knopp), World Scientific Publishing Co., Singapore, 2008.
  • Ramanujan's Lost Notebook, Part II (with G.E. Andrews), Springer, -- --New York (2009).
  • Ramanujan's Lost Notebook, Part III (with G.E. Andrews), Springer, -- --New York (2012).
  • Ramanujan's Lost Notebook, Part IV (with G.E. Andrews), Springer, New York (2013). -->

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    updated 8/23/11