Abels Theorem And the Allied Theory Including the Theory of the Theta Function
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, z p determined by the congruence or, by Provided the places a, x 2, ... , x p be not the zeros of a ^-polynomial, that is, provided none of the places x 2> ... , x p be at a, and there be no coincidence expressible in the form # = #;, the places z lf z 2, ... , z p cannot be coresidual with anyp other places (Chap. VI. 98, and Chap. III. ) and therefore (Chap. VIII. 158) this congruence can only be satisfied when the places z 1} ... , z p are the places Cl, X%, X 3, . . . , X p, these are the...n the zeros of ^ (u), regarded as a function of x^ The two places for which . R has the same value, and y has the same value with opposite signs, are frequently denoted by x and x.
310 EXPRESSION OF THETA QUOTIENTS [206 The zeros of *b(u\u b > a + ...... + u bk > a ) are to be determined by the congruence U x " a i + ...... +U x i a " + U bl > a + ...... + U bk a = U x " a M z " a> ...... U z i a i>, or, by w *i, &i + W *2, x* + ...... + u *p, *i> + M 6, 4. ...... 4. M 6fc, a = 0, which we may write also (z 1} z, ...
What to read after Abels Theorem And the Allied Theory Including the Theory of the Theta Function?
You can find similar books in the "Read Also" column, or choose other free books by Baker, H. F. (Henry Frederick), 1866-1956 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, z p determined by the congruence or, by Provided the places a, x 2, ... , x p be not the zeros of a ^-polynomial, that is, provided none of the places x 2> ... , x p be at a, and there be no coincidence expressible in the form # = #;, the places z lf z 2, ... , z p cannot be coresidual with anyp other places (Chap. VI. 98, and Chap. III. ) and therefore (Chap. VIII. 158) this congruence can only be satisfied when the places z 1} ... , z p are the places Cl, X%, X 3, . . . , X p, these are the...n the zeros of ^ (u), regarded as a function of x^ The two places for which . R has the same value, and y has the same value with opposite signs, are frequently denoted by x and x.
310 EXPRESSION OF THETA QUOTIENTS [206 The zeros of *b(u\u b > a + ...... + u bk > a ) are to be determined by the congruence U x " a i + ...... +U x i a " + U bl > a + ...... + U bk a = U x " a M z " a> ...... U z i a i>, or, by w *i, &i + W *2, x* + ...... + u *p, *i> + M 6, 4. ...... 4. M 6fc, a = 0, which we may write also (z 1} z, ...
What to read after Abels Theorem And the Allied Theory Including the Theory of the Theta Function?
You can find similar books in the "Read Also" column, or choose other free books by Baker, H. F. (Henry Frederick), 1866-1956 to read onlineMoreLess
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