A p-adic analogue of a formula of Ramanujan

[1]  Jeremy A. Rouse Hypergeometric functions and elliptic curves , 2006 .

[2]  Carsten Schneider,et al.  Gaussian Hypergeometric series and supercongruences , 2006, Math. Comput..

[3]  M. Wakayama,et al.  Apéry-like numbers arising from special values of spectral zeta functions for non-commutative harmonic oscillators , 2006, math/0603700.

[4]  M. Papanikolas A formula and a congruence for Ramanujan's -function , 2005 .

[5]  Eric T. Mortenson Supercongruences for truncated n+1Fn hypergeometric series with applications to certain weight three newforms , 2004 .

[6]  Ken Ono,et al.  The web of modularity : arithmetic of the coefficients of modular forms and q-series , 2003 .

[7]  Ken Ono,et al.  A Gaussian hypergeometric series evaluation and Apéry number congruences , 2000 .

[8]  Jonathan M. Borwein,et al.  Pi and the AGM , 1999 .

[9]  J. Borwein,et al.  Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity , 1998 .

[10]  B. Berndt Ramanujan’s Notebooks: Part V , 1997 .

[11]  Dennis Stanton,et al.  A character sum evaluation and Gaussian hypergeometric series , 1986 .

[12]  Jan Stienstra,et al.  On the Picard-Fuchs equation and the formal brauer group of certain ellipticK3-surfaces , 1985 .

[13]  B. Berndt Ramanujan's Notebooks , 1985 .

[14]  Neal Koblitz,et al.  P-adic analysis : a short course on recent work , 1980 .

[15]  A. C. Dixon Summation of a certain Series , 1902 .

[16]  George E. Andrews,et al.  Well-Poised Series , 2009 .

[17]  Eric T. Mortenson,et al.  A p-ADIC SUPERCONGRUENCE CONJECTURE OF VAN HAMME , 2008 .

[18]  Jenny G. Fuselier Hypergeometric Functions Over Finite Fields and Relations to Modular Forms and Elliptic Curves . ( August 2007 ) , 2007 .

[19]  T. Kilbourn An extension of the Apéry number supercongruence , 2006 .

[20]  K. Ono,et al.  Gaussian hypergeometric functions and traces of Hecke operators , 2004 .

[21]  M. Ram Murty,et al.  Introduction to p-adic analytic number theory , 2002 .

[22]  S. Ahlgren Gaussian hypergeometric series and combinatorial congruences , 2001 .

[23]  Frits Beukers,et al.  SPECIAL FUNCTIONS (Encyclopedia of Mathematics and its Applications 71) , 2001 .

[24]  K. Ono Values of Gaussian hypergeometric series , 1998 .

[25]  P. Shiu,et al.  PI AND THE AGM A Study in Analytic Number Theory and Computational Complexity (Canadian Mathematical Society Series of Monographs and Advanced Texts) , 1988 .

[26]  F. Beukers,et al.  A family of K3 surfaces and ζ(3). , 1984 .

[27]  W. N. Bailey,et al.  Generalized hypergeometric series , 1935 .

[28]  G. N. Watson Theorems Stated by Ramanujan (XI) , 1931 .

[29]  C. T. Preece Theorems Stated by Ramanujan (XIII) , 1931 .

[30]  F. J. W. Whipple,et al.  On Well-Poised Series, Generalized Hypergeometric Series having Parameters in Pairs, each Pair with the Same Sum , 1926 .