Generalizing and unifying prior results, we solve the subconvexity problem for the L-functions of GL1 and GL2 automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of…
Number Theory
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This thesis contributes to the analytic theory of automorphic L-functions. We prove an approximate functional equation for the central value of the L-series attached to an irreducible cuspidal automorphic representation of GL(m) over a number field.…
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We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm…
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Lectures on Siegel modular forms given in Nordfjordeid. Besides a survey on Siegel modular forms it presents the joint work with Carel Faber on vector-valued Siegel modular forms of genus 2 and it gives evidence for a conjecture of Harder on…
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The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic…
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Although chemists can synthesize virtually any small organic molecule, our ability to rationally manipulate the structures of proteins is quite limited, despite their involvement in virtually every life process. For most proteins, modifications are…
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Ph.D. StudentScuola Normale Superiore di Pisa -
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