Alen Radolović

A Uniform Rational Critical-Face Theorem for Integer Circulant Determinants of Order 3p and the Pointwise Equivalence at Order 33

For a prime p greater than 3, this preprint compares the first locallyadmissible but globally nonautomatic critical faces 9m and p^2m for integercirculant determinants of order 3p, with m coprime to 3p. An exactnormalization-conductor calculation proves the uniform pointwise tran...

Critical-Face Transfer and Prime Separation for Integer Circulant Determinants of Order 21

Let S(C21) denote the set of determinants of integral 21-by-21 circulantmatrices. This preprint analyzes the first nonautomatic local faces, 9m and49m, for cofactors m coprime to 21. A normalization-conductor calculationgives Pic(Z[C21]) isomorphic to C4 and determines the comple...

A Pointwise 32–p² Critical-Face Equivalence for Circulant Determinants of Order 8p: The Inert Case and Sharpness at p=5

This preprint studies two natural critical valuation faces of integercirculant determinants of order 8p. It shows that when p is a primecongruent to 3 modulo 4, the complete cofactor sets on the 32-face and thep²-face agree point by point, with either determinant sign. The compar...

Davis's Circular-Unit Signature Deficiency: Truncated Minus-Class Fitting Colengths and an Augmented-Ray Formula

This preprint gives a uniform arithmetic interpretation of the polynomialthat computes Davis's circular-unit signature deficiency for primecyclotomic fields. An integral normalization of the odd-residue indexpolynomial is shown to encode truncated lengths of the 2-primary minus-c...

Critical-Face Separation for Integer Circulant Determinants of Order 48: The Least Coprime Separator and Opposite-Direction Ray-Class Families

This preprint studies integer circulant determinants of order 48 and comparestwo natural continuation regimes, represented by values of the form 64m and9m when m is coprime to 6. It develops an exact arithmetic model usingcyclotomic orders, Picard groups, ray-class data, and fini...

Critical-Face Separation for Integer Circulant Determinants of Order 48: The Least Coprime Separator and Opposite-Direction Ray-Class Families

This preprint studies integer circulant determinants of order 48 and comparestwo natural continuation regimes, represented by values of the form 64m and9m when m is coprime to 6. It develops an exact arithmetic model usingcyclotomic orders, Picard groups, ray-class data, and fini...

A Pointwise Critical-Face Transfer for Circulant Determinants of Order 4p

For every odd prime p and every positive integer m coprime to 2p, thispreprint proves that 32m in the order-4p integer circulant-determinant spectrumimplies p^2m in that spectrum, with equivalence when p is congruent to 3modulo 4; the signed form is equivalent by sign symmetry. I...

Integer Group Determinants for C2 x C14: An Exact Hadamard–Conductor Classification

This preprint gives a complete effective classification of the integer group determinants for C2 x C14, equivalently C2^2 x C7. It derives the exact Walsh–Hadamard normalization image and conductor, reduces arbitrary-integer membership to a finite necessary-and-sufficient ideal-a...

Integer Circulant Determinants of Order 28

This preprint gives a complete effective classification of the determinants of 28 by 28 circulant matrices with integer entries. Writing |D| = 2^a 7^b m with gcd(m,14)=1, it proves the exact local floors, identifies (a,b)=(5,0) and (0,2) as the only exceptional faces, and proves...

Integer Circulant Determinants of Order 20

For F in Z[X], set M_20(F) = Res(X^20 − 1, F) and S_20 = {M_20(F) : F in Z[X]}. This preprint determines S_20 completely. Write a nonzero integer as D = ±2^a 5^b m, where m ≥ 1 and gcd(m,10) = 1. The local conditions a = 0 or a ≥ 4 and b = 0 or b ≥ 2 are sufficient except on exac...

Semiprime-Order Circulant Determinants: A Conductor-65 Counterexample, Reciprocal Unit Bases, and a Prime-Norm Classification

This preprint addresses three questions raised by Paudel and Pinner concerning integer circulant determinants of semiprime order. It proves that ±5³ and ±13³ do not occur at order 65, establishes a reciprocal and skew-reciprocal unit-basis theorem for odd cyclotomic fields, and c...

Semiprime-Order Circulant Determinants: A Conductor-65 Counterexample, Reciprocal Unit Bases, and a Prime-Norm Classification

This preprint addresses three questions raised by Paudel and Pinner concerning integer circulant determinants of semiprime order. It proves that ±5³ and ±13³ do not occur at order 65, establishes a reciprocal and skew-reciprocal unit-basis theorem for odd cyclotomic fields, and c...