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Results tagged with exponential-sums
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user 101025
The method of exponential sums is one of a few general methods enabling us to solve a wide range of miscellaneous problems from the theory of numbers and its applications. The strongest results have been obtained with the aid of this method. Therefore knowledge of the fundamentals of theory of exponential sums is necessary for studying modern number theory.
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Conditional convergence of exponential sums related to a Hecke modular form
Definition
Consider the Fourier coefficients $\psi(n)$ of the modular form $\eta^4(6\tau)$,
which are defined in terms of $q=\exp(i2\pi\tau)$ by the identity:
$$\eta^4(6\tau) = q \prod_1^\infty (1-q^ …
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Conditional convergence of exponential sums related to a Hecke modular form
Let me sum up my current state of knowledge.
First, here are some known facts about the coefficients $\psi(n)$ taken from the 1975 article by Ligozat called Courbes modulaires de genre 1.
Théorème B …