Ashoka University is a private university located in Sonipat, Haryana, India, focusing on liberal arts and sciences. It was established in 2014.&nbsp;It is guided by an academic council of academics and scholars from around the world. The council sets the university&#39;s academic standard, advising on matters of curriculum, faculty hiring and research.&nbsp;

Ashoka University offers a full-time 3 (+ 1) year undergraduate programme. The University comprises of&nbsp;2500 plus students, with a mix of both national and international students.&nbsp; &nbsp;

&nbsp;

&nbsp;

Ashoka University

We establish an analogue of the classical Polya–Vinogradov inequality for 𝐺𝐿(2,𝔽𝑝)<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><msub><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">F</mi></mrow></mrow><mi>p</mi></msub><mo stretchy="false">)</mo></math>, where p is a prime. In the process, we compute the ‘singular’ Gauss sums for 𝐺𝐿(2,𝔽𝑝)<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><msub><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">F</mi></mrow></mrow><mi>p</mi></msub><mo stretchy="false">)</mo></math>. As an application, we show that the collection of elements in 𝐺𝐿(2,ℤ)<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow><mo stretchy="false">)</mo></math>&nbsp;whose reduction modulo p are of maximal order in 𝐺𝐿(2,𝔽𝑝)<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><msub><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">F</mi></mrow></mrow><mi>p</mi></msub><mo stretchy="false">)</mo></math>&nbsp;and whose matrix entries are bounded by x has the expected size as soon as 𝑥≫𝑝1/2+ε<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≫</mo><msup><mi>p</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mtext>ε</mtext></mrow></mrow></msup></math>&nbsp;for any ε&gt;0<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mtext>ε</mtext></mrow><mo>&gt;</mo><mn>0</mn></math>.