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Electronic ISBN:  9781470420390 
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Book DetailsContemporary MathematicsVolume: 627; 2014; 174 ppMSC: Primary 05; 11; 14; 17; 30; 33;
This volume contains the proceedings of an international conference to commemorate the 125th anniversary of Ramanujan's birth, held from November 5–7, 2012, at the University of Florida, Gainesville, Florida.
Srinivasa Ramanujan was India's most famous mathematician. This volume contains research and survey papers describing recent and current developments in the areas of mathematics influenced by Ramanujan. The topics covered include modular forms, mock theta functions and harmonic Maass forms, continued fractions, partition inequalities, \(q\)series, representations of affine Lie algebras and partition identities, highly composite numbers, analytic number theory and quadratic forms.ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

Articles

Scott Ahlgren and Nickolas Andersen  Hecke grids and congruences for weakly holomorphic modular forms

George E. Andrews  Knots and $q$series

Alexander Berkovich and Keith Grizzell  A partition inequality involving products of two $q$Pochhammer symbols

Bruce C. Berndt, Sun Kim and Alexandru Zaharescu  Analogues of Koshliakov’s formula

Gaurav Bhatnagar  How to prove Ramanujan’s $q$continued fractions

H. M. Farkas, J. Y. Kaminski and E. Yakubov  A nonsingular $Z_3$ curve of genus $4$

Amanda Folsom, Ken Ono and Robert C. Rhoades  Ramanujan’s radial limits

Michael D. Hirschhorn  An identity that may have changed the course of history

C. Krattenthaler and M. J. Schlosser  The major index generating function of standard Young tableaux of shapes of the form “staircase minus rectangle”

Lisa Lorentzen  Convergence of random continued fractions

Kailash C. Misra and Evan A. Wilson  Tensor product decomposition of $\widehat {\mathfrak {sl}}(n)$ modules and identities

JeanLouis Nicolas and Jonathan Sondow  Ramanujan, Robin, highly composite numbers, and the Riemann Hypothesis

Cherngtiao Perng  A quaternionic proof of the representation formulas of two quaternary quadratic forms


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This volume contains the proceedings of an international conference to commemorate the 125th anniversary of Ramanujan's birth, held from November 5–7, 2012, at the University of Florida, Gainesville, Florida.
Srinivasa Ramanujan was India's most famous mathematician. This volume contains research and survey papers describing recent and current developments in the areas of mathematics influenced by Ramanujan. The topics covered include modular forms, mock theta functions and harmonic Maass forms, continued fractions, partition inequalities, \(q\)series, representations of affine Lie algebras and partition identities, highly composite numbers, analytic number theory and quadratic forms.
Graduate students and research mathematicians interested in number theory.

Articles

Scott Ahlgren and Nickolas Andersen  Hecke grids and congruences for weakly holomorphic modular forms

George E. Andrews  Knots and $q$series

Alexander Berkovich and Keith Grizzell  A partition inequality involving products of two $q$Pochhammer symbols

Bruce C. Berndt, Sun Kim and Alexandru Zaharescu  Analogues of Koshliakov’s formula

Gaurav Bhatnagar  How to prove Ramanujan’s $q$continued fractions

H. M. Farkas, J. Y. Kaminski and E. Yakubov  A nonsingular $Z_3$ curve of genus $4$

Amanda Folsom, Ken Ono and Robert C. Rhoades  Ramanujan’s radial limits

Michael D. Hirschhorn  An identity that may have changed the course of history

C. Krattenthaler and M. J. Schlosser  The major index generating function of standard Young tableaux of shapes of the form “staircase minus rectangle”

Lisa Lorentzen  Convergence of random continued fractions

Kailash C. Misra and Evan A. Wilson  Tensor product decomposition of $\widehat {\mathfrak {sl}}(n)$ modules and identities

JeanLouis Nicolas and Jonathan Sondow  Ramanujan, Robin, highly composite numbers, and the Riemann Hypothesis

Cherngtiao Perng  A quaternionic proof of the representation formulas of two quaternary quadratic forms