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Book
ISBN: 9783034802734 3034802730 Year: 2011 Publisher: Basel : Birkhäuser,
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ISBN: 1281373036 9786611373030 9812772391 9789812772398 981270504X 9789812705044 9781281373038 Year: 2007 Publisher: Singapore Hackensack, N.J. World Scientific
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Collects papers written by many of the world's top experts on L-functions. This work not only covers a range of topics from algebraic and analytic number theories, automorphic forms, to geometry and mathematical physics, but also treats the theory as a whole. It also includes contributions that reflect the most important aspects of L-functions.
Book
ISBN: 147047350X Year: 2023 Publisher: Providence, RI : American Mathematical Society,
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"For a fairly general family of L-functions, we survey the known consequences of the existence of asymptotic formulas with power-saving error term for the (twisted) first and second moments of the central values in the family. We then consider in detail the important special case of the family of twists of a fixed cusp form by primitive Dirichlet characters modulo a prime q, and prove that it satisfies such formulas. We derive arithmetic consequences: a positive proportion of central values L(f [circled x] X, 1/2) are non-zero, and indeed bounded from below; there exist many characters X for which the central L-value is very large; the probability of a large analytic rank decays exponentially fast. We finally show how the second moment estimate establishes a special case of a conjecture of Mazur and Rubin concerning the distribution of modular symbols"--
ISBN: 0691123306 Year: 2005 Publisher: Princeton Princeton University Press
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L-functions --- Monodromy groups --- Sheaf theory
Book
ISBN: 1283433397 9786613433398 9814304999 9789814304993 9789814304986 9814304980 9781283433396 Year: 2011 Publisher: Singapore : World Scientific Pub.,
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This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of Gelfand-Graev type, or of Fourier-Jacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in
L-functions. --- Automorphic forms. --- Representations of groups.
Book
ISBN: 9780821852422 Year: 2011 Publisher: Providence (R.I.) American Mathematical Society
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Curves, Elliptic --- Forms, Modular --- L-functions --- Number theory
Book
ISBN: 3764330880 Year: 1982 Publisher: Basel Birkhäuser
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Congruences and residues --- Forms, Modular --- L-functions --- Modular curves
Book
ISBN: 9781108691536 9781108703390 1108576451 1108691536 Year: 2020 Publisher: Cambridge Cambridge University Press
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The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.
Functions, Zeta. --- L-functions. --- Number theory. --- Combinatorial number theory.
Book
ISBN: 1470410575 Year: 2013 Publisher: Providence, Rhode Island : American Mathematical Society,
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Siegel domains. --- Modular groups. --- Automorphic forms. --- L-functions.
Book
ISBN: 3540176942 0387176942 3540477616 Year: 1987 Volume: 1245 Publisher: Berlin Heidelberg New York Springer
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Number theory --- 51 --- Mathematics --- L-functions. --- Representations of groups. --- 51 Mathematics
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