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Computational Aspects of Modular Forms and Galois RepresentationsHow One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Bas Edixhoven and Jean-Marc Couveignes (eds)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.001.0001
Subject:
Mathematics, Number Theory

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's ... More

Convolution and EquidistributionSato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Nicholas M. Katz

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.001.0001
Subject:
Mathematics, Number Theory

This book explores an important aspect of number theory—the theory of exponential sums over finite fields and their Mellin transforms—from a new, categorical point of view. The book presents ... More

The Gross-Zagier Formula on Shimura Curves

The Gross-Zagier Formula on Shimura Curves

Xinyi Yuan, Shou-wu Zhang, and Wei Zhang

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155913
eISBN:
9781400845644
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155913.001.0001
Subject:
Mathematics, Number Theory

This comprehensive account of the Gross–Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The ... More

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