# Questions tagged [exponential-sums]

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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### Conjecture about an Exponential Sum

**3**

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### Flow of zeros in the shifted exponential generating function?

**4**

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### Lower bound for some sums of roots of unity

**1**

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### Discrepancy bound of integer tensor product sequence?

**0**

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### Difference between Dirichlet Pigeonhole and Exponential sums bound in particular situation?

**3**

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### Inequality for exponential sum in Dvoretzky 1972

**3**

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### Cancellation in this exponential sum?

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### The minimum of the maximum of a sequence of sinc functions

**1**

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### Coefficients $U_m(n,k)$ in the identity $n^{2m+1}=\sum\limits_{0\leq k \leq m}(-1)^{m-k}U_m(n,k)\cdot n^k$

**4**

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### Explicit numbers with square root cancellation in Weyl's exponential sum

**6**

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### Summing the infinite series $\sum_{k=0}^{\infty} \frac{x^k}{(k!)^2}$ [closed]

**3**

**2**answers

### Proof of the identity $\left\lvert\sum_{j=0}^{p-1}e^{(2\pi i/p)(mj^2+nj)}\right\rvert=\sqrt p$ for $p$ odd prime

**2**

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### Uniform power-saving estimate for an exponential sum

**1**

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### Coefficients in the sum $\sum_{k=0}^{n-1}\sum_{j=0}^{m}A_{j,m}(n-k)^jk^j=n^{2m+1}, \ m=1,2,…$

**0**

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### Closed Form or Special Function Expression for Basic Looking Geometric-Like Sum

**0**

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### On existence of certain primes and integers

**3**

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### Approximating $1_I$, $I\subset \lbrack 0,1\rbrack$, by trigonometric polynomials

**2**

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### Moments of certain exponential sum

**5**

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### Number of solutions for the inequality with square roots

**0**

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### Could a full rank linear system arise from this construction?

**3**

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### Prerequisites to read Katz's Gauss Sums, Kloosterman Sums, and Monodromy Groups

**3**

**2**answers

### How to estimate a mixed character sum $\sum_{h \in \mathbb{Z}/q \mathbb{Z}} \chi(f(h)) e(Ch/q)$?

**2**

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### An exponential sum like the Kloosterman sums

**5**

**1**answer

### Does a Kloosterman sum composed with a rational function exhibit square root cancellation?

**-4**

**1**answer

### Does $\int_{0}^{\infty}e^{-xz}\sum_{n=0}^{\infty}a_{n}\frac{x^n}{n!}dx$ converge for $z>0$ with $a_{n} > n! $, for $ n>1$? [closed]

**0**

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### Jacobi sum with half integers

**0**

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### Exponential sum over polynomial values

**1**

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### How to evaluate this sum of roots of unity with condition to zero

**4**

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### On an observation which relates to the exponential sum $\sum_{n=1}^{[\sqrt{t/2\pi}]} n^{-\frac{1}{2}+it}$

**1**

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### Is this averaged exponential sum over primes small infinitely often?

**2**

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### An exponential sum estimate on small intervals

**1**

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### Upper bound for $ \sum_{p\leq x} a(p)p^{it} $

**0**

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### Bounding exponential sum of the form $\sum_{\mathbf{x} \in (\mathbb{Z}/q \mathbb{Z})^n } \chi_1(x_1)\cdots \chi_n (x_n) e(a F(\mathbf{x})/q)$

**2**

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### Hypotheses for exponent pairs

**7**

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### optimal estimate for generalized Kloosterman sum

**4**

**2**answers

### estimate for a sum of products of Weil's sum

**9**

**1**answer

### exponential sum over variety

**0**

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### On a number theoretic problem

**9**

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### Arguments of exponential sums

**-4**

**1**answer

### How many integers between $\left[2^{2^k}, 2^{2^{k+1}}\right]$? [closed]

**0**

**1**answer

### Counting solutions of a certain diophantine equation

**1**

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### Convergence of a tetration series

**1**

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### Obtaining a “one-term” lower bound from an exponential sum lower bound of Roth

**2**

**1**answer

### Upper bound for an exponential sum in Waring-Goldbach problem

**3**

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### On discrepancy of integer sequences related to Erdos-Turan-Koksma

**-2**

**1**answer

### Solutions to a diophantine system

**2**

**1**answer

### Upper bound for a higher dimensional Ramanujan sum

**7**

**0**answers

### $L^1$ norm of Fourier transform of subset sums

**2**

**2**answers

### Occurrence of simultaneous small remainders?

**4**

**1**answer