What is Known About Zero-th Gaussian Periods of Type (N,r)?

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In summary, the conversation discusses the topic of zero-th Gaussian periods of type (N,r), specifically in cases where N is a product of distinct primes and r = p^s is a power of a prime. The speaker is new to this subject and is seeking information on whether there are any known results for this specific scenario. They also provide a brief explanation of what a zero-th Gaussian period of type (N,r) is in this context.
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burritoloco
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Hi,

I'm new to this subject and wondering if anything is known specifically on the zero-th Gaussian periods of type (N,r), where N is a product of distinct primes and r = p^s is a power of a prime. I know there are some very general results out there, but I haven't seen this so far. Thanks!

In case you don't know what I mean: Let X be the canonical additive character on GF(r) and let N be a divisor of r-1. Then the zero-th Gaussian period of type (N,r) is the sum of the values X(z) where z runs over all the elements of the (unique) multiplicative subgroup of GF(r) with order (r-1)/N.

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I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 

Related to What is Known About Zero-th Gaussian Periods of Type (N,r)?

What are "Zero-th Gaussian periods"?

Zero-th Gaussian periods refer to a type of mathematical function used in the study of number theory and cryptography.

What is the significance of "Zero-th Gaussian periods" in science?

These periods are important in understanding the properties of Gaussian integers and their applications in various fields such as coding theory and signal processing.

How are "Zero-th Gaussian periods" calculated?

The calculation of these periods involves the use of complex numbers and their respective properties in the Gaussian integers field.

What are the applications of "Zero-th Gaussian periods"?

These periods have various applications in fields such as cryptography, coding theory, and signal processing, where they are used to analyze and manipulate data.

Are there any limitations to the use of "Zero-th Gaussian periods"?

As with any mathematical concept, there are limitations to the use of these periods. They may not be applicable in certain scenarios or may require additional calculations and adjustments.

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