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From July 31 through August 3,1997, the Pennsylvania State
University hosted the Topics in Number Theory Conference. The
conference was organized by Ken Ono and myself. By writing the
preface, I am afforded the opportunity to express my gratitude to
Ken for beng the inspiring and driving force behind the whole
conference. Without his energy, enthusiasm and skill the entire
event would never have occurred. We are extremely grateful to the
sponsors of the conference: The National Sci ence Foundation, The
Penn State Conference Center and the Penn State Depart ment of
Mathematics. The object in this conference was to provide a variety
of presentations giving a current picture of recent, significant
work in number theory. There were eight plenary lectures: H. Darmon
(McGill University), "Non-vanishing of L-functions and their
derivatives modulo p. " A. Granville (University of Georgia), "Mean
values of multiplicative functions. " C. Pomerance (University of
Georgia), "Recent results in primality testing. " C. Skinner
(Princeton University), "Deformations of Galois representations. "
R. Stanley (Massachusetts Institute of Technology), "Some
interesting hyperplane arrangements. " F. Rodriguez Villegas
(Princeton University), "Modular Mahler measures. " T. Wooley
(University of Michigan), "Diophantine problems in many variables:
The role of additive number theory. " D. Zeilberger (Temple
University), "Reverse engineering in combinatorics and number
theory. " The papers in this volume provide an accurate picture of
many of the topics presented at the conference including
contributions from four of the plenary lectures."
Robert A. Rankin, one of the world's foremost authorities on
modular forms and a founding editor of The Ramanujan Journal, died
on January 27, 2001, at the age of 85. Rankin had broad interests
and contributed fundamental papers in a wide variety of areas
within number theory, geometry, analysis, and algebra. To
commemorate Rankin's life and work, the editors have collected
together 25 papers by several eminent mathematicians reflecting
Rankin's extensive range of interests within number theory. Many of
these papers reflect Rankin's primary focus in modular forms. It is
the editors' fervent hope that mathematicians will be stimulated by
these papers and gain a greater appreciation for Rankin's
contributions to mathematics.
This volume would be an inspiration to students and researchers in
the areas of number theory and modular forms.
Robert A. Rankin, one of the world's foremost authorities on
modular forms and a founding editor of The Ramanujan Journal, died
on January 27, 2001, at the age of 85. Rankin had broad interests
and contributed fundamental papers in a wide variety of areas
within number theory, geometry, analysis, and algebra. To
commemorate Rankin's life and work, the editors have collected
together 25 papers by several eminent mathematicians reflecting
Rankin's extensive range of interests within number theory. Many of
these papers reflect Rankin's primary focus in modular forms. It is
the editors' fervent hope that mathematicians will be stimulated by
these papers and gain a greater appreciation for Rankin's
contributions to mathematics.
This volume would be an inspiration to students and researchers in
the areas of number theory and modular forms.
From July 31 through August 3,1997, the Pennsylvania State
University hosted the Topics in Number Theory Conference. The
conference was organized by Ken Ono and myself. By writing the
preface, I am afforded the opportunity to express my gratitude to
Ken for beng the inspiring and driving force behind the whole
conference. Without his energy, enthusiasm and skill the entire
event would never have occurred. We are extremely grateful to the
sponsors of the conference: The National Sci ence Foundation, The
Penn State Conference Center and the Penn State Depart ment of
Mathematics. The object in this conference was to provide a variety
of presentations giving a current picture of recent, significant
work in number theory. There were eight plenary lectures: H. Darmon
(McGill University), "Non-vanishing of L-functions and their
derivatives modulo p. " A. Granville (University of Georgia), "Mean
values of multiplicative functions. " C. Pomerance (University of
Georgia), "Recent results in primality testing. " C. Skinner
(Princeton University), "Deformations of Galois representations. "
R. Stanley (Massachusetts Institute of Technology), "Some
interesting hyperplane arrangements. " F. Rodriguez Villegas
(Princeton University), "Modular Mahler measures. " T. Wooley
(University of Michigan), "Diophantine problems in many variables:
The role of additive number theory. " D. Zeilberger (Temple
University), "Reverse engineering in combinatorics and number
theory. " The papers in this volume provide an accurate picture of
many of the topics presented at the conference including
contributions from four of the plenary lectures."
"The son of a prominent Japanese mathematician who came to the
United States after World War II, Ken Ono was raised on a diet of
high expectations and little praise. Rebelling against his
pressure-cooker of a life, Ken determined to drop out of high
school to follow his own path. To obtain his father's approval, he
invoked the biography of the famous Indian mathematical prodigy
Srinivasa Ramanujan, whom his father revered, who had twice flunked
out of college because of his single-minded devotion to
mathematics. Ono describes his rocky path through college and
graduate school, interweaving Ramanujan's story with his own and
telling how at key moments, he was inspired by Ramanujan and guided
by mentors who encouraged him to pursue his interest in exploring
Ramanujan's mathematical legacy. Picking up where others left off,
beginning with the great English mathematician G.H. Hardy, who
brought Ramanujan to Cambridge in 1914, Ono has devoted his
mathematical career to understanding how in his short life,
Ramanujan was able to discover so many deep mathematical truths,
which Ramanujan believed had been sent to him as visions from a
Hindu goddess. And it was Ramanujan who was ultimately the source
of reconciliation between Ono and his parents. Ono's search for
Ramanujan ranges over three continents and crosses paths with
mathematicians whose lives span the globe and the entire twentieth
century and beyond. Along the way, Ken made many fascinating
discoveries. The most important and surprising one of all was his
own humanity."
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